Câu hỏi của Nguyễn Hương Giang

Question

Phân tích đa thức thành nhân tử:

a) 4x4 - 21x2y2 + y4

b) x5 - 5x3 + 4x

c) x3 + 5x2 + 3x - 9

d) x16 + x8  - 2

Akai Haruma · Accepted Answer

a)

$4x^4-21x^2y^2+y^4=(4x^4+4x^2y^2+y^4)-25x^2y^2$

$=(2x^2+y^2)^2-(5xy)^2$

$=(2x^2+y^2-5xy)(2x^2+y^2+5xy)$

b)

$x^5-5x^3+4x=x(x^4-5x^2+4)$

$=x(x^4-x^2-4x^2+4)$

$=x[x^2(x^2-1)-4(x^2-1)]$

$=x(x^2-4)(x^2-1)=x(x-2)(x+2)(x-1)(x+1)$Câu trả lời: a)

$4x^4-21x^2y^2+y^4=(4x^4+4x^2y^2+y^4)-25x^2y^2$

$=(2x^2+y^2)^2-(5xy)^2$

$=(2x^2+y^2-5xy)(2x^2+y^2+5xy)$

b)

$x^5-5x^3+4x=x(x^4-5x^2+4)$

$=x(x^4-x^2-4x^2+4)$

$=x[x^2(x^2-1)-4(x^2-1)]$

$=x(x^2-4)(x^2-1)=x(x-2)(x+2)(x-1)(x+1)$

Akai Haruma · Answer

c)

$x^3+5x^2+3x-9=x^3-x^2+6x^2-6x+9x-9$

$=x^2(x-1)+6x(x-1)+9(x-1)$

$=(x-1)(x^2+6x+9)$

$=(x-1)(x^2+2.3x+3^2)=(x-1)(x+3)^2$

d)

$x^{16}+x^8-2=x^{16}-1^{16}+x^8-1^{16}$

$=(x-1)(x^{15}+x^{14}+...+x+1)+(x-1)(x^7+x^6+...+x+1)$

$=(x-1)(x^{15}+x^{14}+...+x^8+2x^7+2x^6+2x^5+...+2x+2)$Câu trả lời: c)