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<blockquote data-quote="Thandieu2" data-source="post: 140436" data-attributes="member: 1323">Bài tập phân tích đa thức thành nhân tử bằng cách phối hợp nhiều phương phápBÀI TẬP PHÂN TÍCH ĐA THỨC THÀNH NHÂN TỬ BẰNG CÁCH PHỐI HỢP NHIỀU PHƯƠNG PHÁP
1)&nbsp; &nbsp; &nbsp; Phân tích các đa thức sau thành nhân tử:a)&nbsp; &nbsp; &nbsp; a[SUP]3[/SUP] + b[SUP]3[/SUP] + c[SUP]3[/SUP] – 3abcb)&nbsp; &nbsp; &nbsp; (x – y )[SUP]3[/SUP] + (y – z )[SUP]3[/SUP] + (z – x)[SUP]3[/SUP]2)&nbsp; &nbsp; &nbsp; Dùng phương pháp đặt ẩn phụ , phân tích đa thức thành nhân tử:a)&nbsp; &nbsp; &nbsp; (x[SUP]2[/SUP] + x + 1)(x[SUP]2[/SUP] + x + 2) – 12 b)&nbsp; &nbsp; &nbsp; 4x(x + y)(x + y + z )(x + z) + y[SUP]2[/SUP]z[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3) Phân tích đa thức sau thành nhân tử:&nbsp;&nbsp; x[SUP]5[/SUP] + x + 1Giải:&nbsp; &nbsp; &nbsp;&nbsp; [SPOILER]°&nbsp; Cách 1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x[SUP]5[/SUP] + x + 1 = x[SUP]5[/SUP] + x[SUP]4[/SUP] + x[SUP]3[/SUP] – x[SUP]4[/SUP] – x[SUP]3[/SUP] – x[SUP]2[/SUP] + x[SUP]2[/SUP] + x + 1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = x[SUP]3[/SUP](x[SUP]2[/SUP] + x + 1) – x[SUP]2[/SUP](x[SUP]2[/SUP] + x + 1) + 1(x[SUP]2[/SUP] + x + 1)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] + x + 1)(x[SUP]3[/SUP] – x[SUP]2[/SUP] + 1)&nbsp; &nbsp; &nbsp; &nbsp; °&nbsp; Cách 2 : &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x[SUP]5[/SUP] + x + 1 = x[SUP]5[/SUP] – x[SUP]2[/SUP] + x[SUP]2[/SUP] + x + 1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = x[SUP]2[/SUP](x[SUP]3[/SUP] – 1) + 1(x[SUP]2[/SUP] + x + 1)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = x[SUP]2[/SUP](x – 1)(x[SUP]2[/SUP] + x + 1) + 1(x[SUP]2[/SUP] + x + 1)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] + x + 1)[(x[SUP]2[/SUP](x – 1) + 1]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] + x + 1)[x[SUP]3[/SUP] – x[SUP]2[/SUP] + 1)[/SPOILER]4)Phân tích đa thức sau thành nhân tử : x[SUP]2[/SUP] – 8x + 12[SPOILER]Giải:&nbsp; &nbsp; &nbsp; &nbsp; °&nbsp; Cách 1:&nbsp; &nbsp; x[SUP]2[/SUP] – 8x + 12 = x[SUP]2[/SUP] – 2x – 6x + 12&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] – 2x) – (6x – 12)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = x(x – 2) – 6(x – 2)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 2)(x – 6) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 2 :&nbsp; &nbsp; x[SUP]2[/SUP] – 8x + 12 = (x[SUP]2[/SUP] – 8x + 16) – 4 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 4)[SUP]2[/SUP] - 2[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 4 + 2)(x – 4 – 2 )&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 2 )(x – 6)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 3 :&nbsp;&nbsp; x[SUP]2[/SUP] – 8x + 12 = x[SUP]2[/SUP] – 36 – 8x + 48&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] – 36) – (8x – 48)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x + 6)(x – 6) – 8(x – 6)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 6)(x + 6 – 8)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 6)(x – 2)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; °&nbsp; Cách 4 :&nbsp;&nbsp; x[SUP]2[/SUP] – 8x + 12&nbsp; =&nbsp; x[SUP]2[/SUP] – 4 – 8x + 16&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] – 4) – (8x – 16)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x + 2)(x – 2) – 8(x – 2)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 2)(x + 2 – 8)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 2)(x – 6)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; °&nbsp; Cách 5:&nbsp;&nbsp; x[SUP]2[/SUP] – 8x + 12&nbsp; =&nbsp;&nbsp; x[SUP]2[/SUP] – 4x + 4 – 4x + 8 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] – 4x + 4) – (4x – 8)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 2)[SUP]2[/SUP] – 4(x – 2)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 2)(x – 2 – 4)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x – 2)(x – 6)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; °&nbsp; Cách 6:&nbsp; x[SUP]2[/SUP] – 8x + 12&nbsp;&nbsp; =&nbsp; x[SUP]2[/SUP] – 12x + 36 + 4x – 24 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x[SUP]2[/SUP] – 12x + 36) + (4x – 24)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x – 6)[SUP]2[/SUP] + 4(x – 6)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x – 6)(x – 6 + 4)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x – 6)(x – 2)[/SPOILER]&nbsp;5)Phân tích đa thức sau thành nhân tử :&nbsp; x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP]Giải:&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [SPOILER]°&nbsp; Cách 1:&nbsp; x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] + xy + 3xy + + 3y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (x[SUP]2[/SUP] + xy) + (3xy + + 3y[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = x(x + y) + 3y(x + y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)(x + 3y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 2 : x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] =&nbsp; x[SUP]2[/SUP] + 4xy + 4y[SUP]2[/SUP] – y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x[SUP]2[/SUP] + 4xy + 4y[SUP]2[/SUP]) – y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 2y)[SUP]2[/SUP] – y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 2y + y)(x + 2y – y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 3y)(x + y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 3 : x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] – y[SUP]2[/SUP] + 4xy + 4y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x[SUP]2[/SUP] – y[SUP]2[/SUP]) + ( 4xy + 4y[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)(x – y) + 4y(x + y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)(x – y + 4y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)(x + 3y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 4 : x[SUP]2[/SUP] + 4xy + 3y[SUP]2 [/SUP]= x[SUP]2[/SUP] – 9y[SUP]2[/SUP] + 4xy + 12y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x[SUP]2[/SUP] – 9y[SUP]2[/SUP]) + (4xy + 12y[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 3y)(x – 3y) + 4y(x + 3y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 3y)(x – 3y + 4y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 3y)(x + y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 5 : x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] + 2xy + y[SUP]2[/SUP] + 2xy + 2y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x[SUP]2[/SUP] + 2xy + y[SUP]2[/SUP]) + (2xy + 2y[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)[SUP]2[/SUP] + 2y(x + y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)(x + y + 2y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)( x + 3y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 6 : x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] + 6xy + 9y[SUP]2[/SUP] – 2xy – 6y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x[SUP]2[/SUP] + 6xy + 9y[SUP]2[/SUP]) – (2xy + 6y[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 3y)[SUP]2[/SUP] – 2y(x + 3y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 3y)(x + 3y – 2y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + 3y)(x + y)&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; °&nbsp; Cách 7 : x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = 4x[SUP]2[/SUP] + 4xy – 3x[SUP]2[/SUP] + 3y[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (4x[SUP]2[/SUP] + 4xy) – (3x[SUP]2[/SUP] – 3y[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 4x(x + y) – 3(x + y)(x – y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)(4x – 3x + 3y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (x + y)(x + 3y)[/SPOILER]6) Phân tích đa thức sau thành nhân tử: a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP](c[SUP]2[/SUP] – a[SUP]2[/SUP]) + c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP])Giải:[SPOILER]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; °&nbsp; Cách 1:&nbsp; &nbsp; &nbsp; a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP](c[SUP]2[/SUP] – a[SUP]2[/SUP]) + c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP]) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP][(c[SUP]2[/SUP] – b[SUP]2[/SUP]) – (a[SUP]2[/SUP] – b[SUP]2[/SUP]) ] + c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP](c[SUP]2[/SUP] – b[SUP]2[/SUP]) – b[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP]) +&nbsp; c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (b[SUP]2[/SUP] – c[SUP]2[/SUP])(a[SUP]3[/SUP] – b[SUP]3[/SUP]) – (a[SUP]2[/SUP] – b[SUP]2[/SUP])(b[SUP]3[/SUP] – c[SUP]3[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (b + c)(b – c)(a – b)(a[SUP]2[/SUP] + ab + b[SUP]2[/SUP]) – (a + b)(a – b)(b – c)(b[SUP]2[/SUP] + bc + c[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (a – b)(b – c)[(b + c)(a[SUP]2[/SUP] + ab + b[SUP]2[/SUP]) – (a + b)( b[SUP]2[/SUP] + bc + c[SUP]2[/SUP])]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (a – b)(b – c)(a[SUP]2[/SUP]b + ab[SUP]2 [/SUP]+ b[SUP]3[/SUP] + a[SUP]2[/SUP]c + abc + b[SUP]2[/SUP]c – ab[SUP]2[/SUP] – abc – ac[SUP]2[/SUP] – b[SUP]3[/SUP] – b[SUP]2[/SUP]c – bc[SUP]2[/SUP]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (a – b)(b – c)(a[SUP]2[/SUP]b + a[SUP]2[/SUP]c – bc[SUP]2[/SUP] – ac[SUP]2[/SUP])&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (a – b)(b – c)[b(a[SUP]2[/SUP] – c[SUP]2[/SUP])&nbsp; + ac(a – c)]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (a – b)(b – c)[b(a – c)(a + c) + ac(a – c)]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; = (a – b)(b – c)(a – c)(ab + bc + ac)[/SPOILER]7) Tìm x , biết :a)&nbsp; &nbsp; &nbsp; (2x – 1)[SUP]2[/SUP] – (x +3)[SUP]2[/SUP] = 0b)&nbsp; &nbsp; &nbsp; 5x(x – 3) + 3 – x = 08) Tìm x , biết :a)&nbsp; &nbsp; &nbsp; (5 – 2x)(2x + 7) = 4x[SUP]2[/SUP] – 25b)&nbsp; &nbsp; &nbsp; x[SUP]3[/SUP] + 27 + (x + 3)(x – 9) = 0c)&nbsp; &nbsp; &nbsp; 4(2x + 7) – 9(x + 3)[SUP]2[/SUP] = 0d)&nbsp; &nbsp;&nbsp; (5x[SUP]2[/SUP] + 3x – 2 )[SUP]2[/SUP] = (4x[SUP]2[/SUP] – 3x – 2 )[SUP]2[/SUP] Đề xuất bài tập :&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1) Phân tích các đa thức sau thành nhân tử :&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; a) x[SUP]5 [/SUP]– x[SUP]4[/SUP] – x[SUP]3[/SUP] – x[SUP]2[/SUP] – x – 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; b) x[SUP]8[/SUP] + x[SUP]6 [/SUP] + x[SUP]4[/SUP] + x[SUP]2[/SUP] + 1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; c) x[SUP]8[/SUP] + x[SUP]7[/SUP] + 1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d) x[SUP]9[/SUP] – x[SUP]7[/SUP] – x[SUP]6[/SUP] – x[SUP]5[/SUP] + x[SUP]4[/SUP] + x[SUP]3[/SUP] + x[SUP]2[/SUP] + x + 1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2) Phân tích các đa thức sau thành nhân tử bằng phương pháp đặt ẩn phụ :&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; a) (x[SUP]2[/SUP] + x)[SUP]2[/SUP] – 2(x[SUP]2[/SUP] + x) – 15 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; b) (x + 2)(x + 3)(x + 4)(x + 5) – 24 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; c) (x[SUP]2[/SUP] + 8x + 7)( x[SUP]2[/SUP] + 8x + 15) + 15&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d) (x[SUP]2[/SUP] + 3x + 1)( x[SUP]2[/SUP] + 3x + 2) – 6 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3) Phân tích các đa thức sau thành nhân tử bằng phương pháp thêm, bớt hoặc tách các hạng tử: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; a) bc(b + c) + ca(c – a) – ab(a + b)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; b) 2a[SUP]2[/SUP]b + 4ab[SUP]2[/SUP] – a[SUP]2[/SUP]c + ac[SUP]2[/SUP] – 4b[SUP]2[/SUP]c + 2bc[SUP]2[/SUP] – 4abc &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; c) y(x – 2z)[SUP]2[/SUP] + 8xyz + x(y – 2z)[SUP]2[/SUP] – 2z(x + y)[SUP]2[/SUP]</blockquote>

[QUOTE="Thandieu2, post: 140436, member: 1323"] [b]Bài tập phân tích đa thức thành nhân tử bằng cách phối hợp nhiều phương pháp[/b] [CENTER][FONT=arial][B]BÀI TẬP PHÂN TÍCH ĐA THỨC THÀNH NHÂN TỬ BẰNG CÁCH PHỐI HỢP NHIỀU PHƯƠNG PHÁP [/B][/FONT][/CENTER] [FONT=arial][B] 1) [/B][B]Phân tích các đa thức sau thành nhân tử:[/B] a) a[SUP]3[/SUP] + b[SUP]3[/SUP] + c[SUP]3[/SUP] – 3abc b) (x – y )[SUP]3[/SUP] + (y – z )[SUP]3[/SUP] + (z – x)[SUP]3 [/SUP][B] 2) [/B][B]Dùng phương pháp đặt ẩn phụ , phân tích đa thức thành nhân tử:[/B] a) (x[SUP]2[/SUP] + x + 1)(x[SUP]2[/SUP] + x + 2) – 12 b) 4x(x + y)(x + y + z )(x + z) + y[SUP]2[/SUP]z[SUP]2 [/SUP] [B] 3) Phân tích đa thức sau thành nhân tử: [/B]x[SUP]5[/SUP] + x + 1 [B][U]Giải:[/U][/B] [SPOILER]° [B]Cách 1[/B] x[SUP]5[/SUP] + x + 1 = x[SUP]5[/SUP] + x[SUP]4[/SUP] + x[SUP]3[/SUP] – x[SUP]4[/SUP] – x[SUP]3[/SUP] – x[SUP]2[/SUP] + x[SUP]2[/SUP] + x + 1 = x[SUP]3[/SUP](x[SUP]2[/SUP] + x + 1) – x[SUP]2[/SUP](x[SUP]2[/SUP] + x + 1) + 1(x[SUP]2[/SUP] + x + 1) = (x[SUP]2[/SUP] + x + 1)(x[SUP]3[/SUP] – x[SUP]2[/SUP] + 1) ° [B]Cách 2 : [/B] x[SUP]5[/SUP] + x + 1 = x[SUP]5[/SUP] – x[SUP]2[/SUP] + x[SUP]2[/SUP] + x + 1 = x[SUP]2[/SUP](x[SUP]3[/SUP] – 1) + 1(x[SUP]2[/SUP] + x + 1) = x[SUP]2[/SUP](x – 1)(x[SUP]2[/SUP] + x + 1) + 1(x[SUP]2[/SUP] + x + 1) = (x[SUP]2[/SUP] + x + 1)[(x[SUP]2[/SUP](x – 1) + 1] = (x[SUP]2[/SUP] + x + 1)[x[SUP]3[/SUP] – x[SUP]2[/SUP] + 1)[/SPOILER] [B]4)Phân tích đa thức sau thành nhân tử :[/B] x[SUP]2[/SUP] – 8x + 12 [SPOILER][B][U]Giải:[/U][/B] ° [B]Cách 1: [/B] x[SUP]2[/SUP] – 8x + 12 = x[SUP]2[/SUP] – 2x – 6x + 12 = (x[SUP]2[/SUP] – 2x) – (6x – 12) = x(x – 2) – 6(x – 2) = (x – 2)(x – 6) ° [B]Cách 2 : [/B]x[SUP]2[/SUP] – 8x + 12 = (x[SUP]2[/SUP] – 8x + 16) – 4 = (x – 4)[SUP]2[/SUP] - 2[SUP]2[/SUP] = (x – 4 + 2)(x – 4 – 2 ) = (x – 2 )(x – 6) ° [B]Cách 3 : [/B]x[SUP]2[/SUP] – 8x + 12 = x[SUP]2[/SUP] – 36 – 8x + 48 = (x[SUP]2[/SUP] – 36) – (8x – 48) = (x + 6)(x – 6) – 8(x – 6) = (x – 6)(x + 6 – 8) = (x – 6)(x – 2) ° [B]Cách 4 : [/B]x[SUP]2[/SUP] – 8x + 12 = x[SUP]2[/SUP] – 4 – 8x + 16 = (x[SUP]2[/SUP] – 4) – (8x – 16) = (x + 2)(x – 2) – 8(x – 2) = (x – 2)(x + 2 – 8) = (x – 2)(x – 6) ° [B]Cách 5: [/B]x[SUP]2[/SUP] – 8x + 12 = x[SUP]2[/SUP] – 4x + 4 – 4x + 8 = (x[SUP]2[/SUP] – 4x + 4) – (4x – 8) = (x – 2)[SUP]2[/SUP] – 4(x – 2) = (x – 2)(x – 2 – 4) = (x – 2)(x – 6) ° [B]Cách 6: [/B]x[SUP]2[/SUP] – 8x + 12 = x[SUP]2[/SUP] – 12x + 36 + 4x – 24 = (x[SUP]2[/SUP] – 12x + 36) + (4x – 24) = (x – 6)[SUP]2[/SUP] + 4(x – 6) = (x – 6)(x – 6 + 4) = (x – 6)(x – 2)[/SPOILER] [B]5)Phân tích đa thức sau thành nhân tử :[/B] x[SUP]2[/SUP] + 4xy + 3y[SUP]2 [/SUP] [B][U]Giải:[/U][/B] [SPOILER]° [B]Cách 1: [/B]x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] + xy + 3xy + + 3y[SUP]2[/SUP] = (x[SUP]2[/SUP] + xy) + (3xy + + 3y[SUP]2[/SUP]) = x(x + y) + 3y(x + y) = (x + y)(x + 3y) ° [B]Cách 2 : [/B]x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] + 4xy + 4y[SUP]2[/SUP] – y[SUP]2[/SUP] = (x[SUP]2[/SUP] + 4xy + 4y[SUP]2[/SUP]) – y[SUP]2[/SUP] = (x + 2y)[SUP]2[/SUP] – y[SUP]2[/SUP] = (x + 2y + y)(x + 2y – y) = (x + 3y)(x + y) ° [B]Cách 3 : [/B]x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] – y[SUP]2[/SUP] + 4xy + 4y[SUP]2[/SUP] = (x[SUP]2[/SUP] – y[SUP]2[/SUP]) + ( 4xy + 4y[SUP]2[/SUP]) = (x + y)(x – y) + 4y(x + y) = (x + y)(x – y + 4y) = (x + y)(x + 3y) ° [B]Cách 4 : [/B]x[SUP]2[/SUP] + 4xy + 3y[SUP]2 [/SUP]= x[SUP]2[/SUP] – 9y[SUP]2[/SUP] + 4xy + 12y[SUP]2[/SUP] = (x[SUP]2[/SUP] – 9y[SUP]2[/SUP]) + (4xy + 12y[SUP]2[/SUP]) = (x + 3y)(x – 3y) + 4y(x + 3y) = (x + 3y)(x – 3y + 4y) = (x + 3y)(x + y) ° [B]Cách 5 : [/B]x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] + 2xy + y[SUP]2[/SUP] + 2xy + 2y[SUP]2[/SUP] = (x[SUP]2[/SUP] + 2xy + y[SUP]2[/SUP]) + (2xy + 2y[SUP]2[/SUP]) = (x + y)[SUP]2[/SUP] + 2y(x + y) = (x + y)(x + y + 2y) = (x + y)( x + 3y) ° [B]Cách 6 : [/B]x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = x[SUP]2[/SUP] + 6xy + 9y[SUP]2[/SUP] – 2xy – 6y[SUP]2[/SUP] = (x[SUP]2[/SUP] + 6xy + 9y[SUP]2[/SUP]) – (2xy + 6y[SUP]2[/SUP]) = (x + 3y)[SUP]2[/SUP] – 2y(x + 3y) = (x + 3y)(x + 3y – 2y) = (x + 3y)(x + y) ° [B]Cách 7 : [/B]x[SUP]2[/SUP] + 4xy + 3y[SUP]2[/SUP] = 4x[SUP]2[/SUP] + 4xy – 3x[SUP]2[/SUP] + 3y[SUP]2[/SUP] = (4x[SUP]2[/SUP] + 4xy) – (3x[SUP]2[/SUP] – 3y[SUP]2[/SUP]) = 4x(x + y) – 3(x + y)(x – y) = (x + y)(4x – 3x + 3y) = (x + y)(x + 3y)[/SPOILER] [B]6) Phân tích đa thức sau thành nhân tử: [/B]a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP](c[SUP]2[/SUP] – a[SUP]2[/SUP]) + c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP]) [/FONT][B][U] Giải:[/U][/B][FONT=arial] [SPOILER] ° [B]Cách 1: [/B]a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP](c[SUP]2[/SUP] – a[SUP]2[/SUP]) + c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP]) = a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP][(c[SUP]2[/SUP] – b[SUP]2[/SUP]) – (a[SUP]2[/SUP] – b[SUP]2[/SUP]) ] + c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP]) = a[SUP]3[/SUP](b[SUP]2[/SUP] – c[SUP]2[/SUP]) + b[SUP]3[/SUP](c[SUP]2[/SUP] – b[SUP]2[/SUP]) – b[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP]) + c[SUP]3[/SUP](a[SUP]2[/SUP] – b[SUP]2[/SUP]) = (b[SUP]2[/SUP] – c[SUP]2[/SUP])(a[SUP]3[/SUP] – b[SUP]3[/SUP]) – (a[SUP]2[/SUP] – b[SUP]2[/SUP])(b[SUP]3[/SUP] – c[SUP]3[/SUP]) = (b + c)(b – c)(a – b)(a[SUP]2[/SUP] + ab + b[SUP]2[/SUP]) – (a + b)(a – b)(b – c)(b[SUP]2[/SUP] + bc + c[SUP]2[/SUP]) = (a – b)(b – c)[(b + c)(a[SUP]2[/SUP] + ab + b[SUP]2[/SUP]) – (a + b)( b[SUP]2[/SUP] + bc + c[SUP]2[/SUP])] = (a – b)(b – c)(a[SUP]2[/SUP]b + ab[SUP]2 [/SUP]+ b[SUP]3[/SUP] + a[SUP]2[/SUP]c + abc + b[SUP]2[/SUP]c – ab[SUP]2[/SUP] – abc – ac[SUP]2[/SUP] – b[SUP]3[/SUP] – b[SUP]2[/SUP]c – bc[SUP]2[/SUP] = (a – b)(b – c)(a[SUP]2[/SUP]b + a[SUP]2[/SUP]c – bc[SUP]2[/SUP] – ac[SUP]2[/SUP]) = (a – b)(b – c)[b(a[SUP]2[/SUP] – c[SUP]2[/SUP]) + ac(a – c)] = (a – b)(b – c)[b(a – c)(a + c) + ac(a – c)] = (a – b)(b – c)(a – c)(ab + bc + ac)[/SPOILER] [B] 7) Tìm x , biết :[/B] a) (2x – 1)[SUP]2[/SUP] – (x +3)[SUP]2[/SUP] = 0 b) 5x(x – 3) + 3 – x = 0 [B] 8) Tìm x , biết :[/B] a) (5 – 2x)(2x + 7) = 4x[SUP]2[/SUP] – 25 b) x[SUP]3[/SUP] + 27 + (x + 3)(x – 9) = 0 c) 4(2x + 7) – 9(x + 3)[SUP]2[/SUP] = 0 d) (5x[SUP]2[/SUP] + 3x – 2 )[SUP]2[/SUP] = (4x[SUP]2[/SUP] – 3x – 2 )[SUP]2[/SUP] [B] Đề xuất bài tập : [/B] [B]1) Phân tích các đa thức sau thành nhân tử : [/B] a) x[SUP]5 [/SUP]– x[SUP]4[/SUP] – x[SUP]3[/SUP] – x[SUP]2[/SUP] – x – 2 b) x[SUP]8[/SUP] + x[SUP]6 [/SUP] + x[SUP]4[/SUP] + x[SUP]2[/SUP] + 1 c) x[SUP]8[/SUP] + x[SUP]7[/SUP] + 1 d) x[SUP]9[/SUP] – x[SUP]7[/SUP] – x[SUP]6[/SUP] – x[SUP]5[/SUP] + x[SUP]4[/SUP] + x[SUP]3[/SUP] + x[SUP]2[/SUP] + x + 1 [B]2) Phân tích các đa thức sau thành nhân tử bằng phương pháp đặt ẩn phụ : [/B] a) (x[SUP]2[/SUP] + x)[SUP]2[/SUP] – 2(x[SUP]2[/SUP] + x) – 15 b) (x + 2)(x + 3)(x + 4)(x + 5) – 24 c) (x[SUP]2[/SUP] + 8x + 7)( x[SUP]2[/SUP] + 8x + 15) + 15 d) (x[SUP]2[/SUP] + 3x + 1)( x[SUP]2[/SUP] + 3x + 2) – 6 [B]3) Phân tích các đa thức sau thành nhân tử bằng phương pháp thêm, bớt hoặc tách các hạng tử: [/B] a) bc(b + c) + ca(c – a) – ab(a + b) b) 2a[SUP]2[/SUP]b + 4ab[SUP]2[/SUP] – a[SUP]2[/SUP]c + ac[SUP]2[/SUP] – 4b[SUP]2[/SUP]c + 2bc[SUP]2[/SUP] – 4abc c) y(x – 2z)[SUP]2[/SUP] + 8xyz + x(y – 2z)[SUP]2[/SUP] – 2z(x + y)[SUP]2[/SUP][/FONT] [/QUOTE]

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