Question

Bài 2 : Phân tích các đa thức thành nhân tử :
a, x^4 - 2x^3 + 2x - 1
b, a^6 - a^4 + 2a^3 + 2a^2
c, x^4 + x^3 + 2x^2 + x + 1
d, x^4 + 2x^3 + 2x^2 + 2x + 1
e, x^2y + xy^2 + x^2z + y^2z + 2xyz
f, x^5 + x^4 + x^3 + x^2 + x + 1
Giúp mk vs ạ mk cần gấp ạ

Answer 1

a)

$x^4-2x^3+2x-1=(x^4-2x^3+x^2)-(x^2-2x+1)$

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

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

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

b)

$a^6-a^4+2a^3+2a^2$

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

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

$=(a+1)[a^4(a-1)+2a^2]$

$=a^2(a+1)[a^2(a-1)+2]$

$=a^2(a+1)(a^3-a^2+2)=a^2(a+1)[a^2(a+1)-2(a^2-1)]$

$=a^2(a+1)[a^2(a+1)-2(a-1)(a+1)]$

$=a^2(a+1)(a+1)(a^2-2a+2)=a^2(a+1)^2(a^2-2a+2)$

c)

$x^4+x^3+2x^2+x+1$

$=(x^4+2x^2+1)+(x^3+x)$

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

Answer 2

d)

$x^4+2x^3+2x^2+2x+1$

$=(x^4+2x^3+x^2)+(x^2+2x+1)$

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

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

e)

$x^2y+xy^2+x^2z+y^2z+2xyz$

$=xy(x+y)+z(x^2+y^2)+2xyz$

$=xy(x+y)+z(x^2+y^2+2xy)$

$=xy(x+y)+z(x+y)^2=(x+y)(xy+zx+zy)$

f)

$x^5+x^4+x^3+x^2+x+1$

$=(x^5+x^4)+(x^3+x^2)+(x+1)=x^4(x+1)+x^2(x+1)+(x+1)$

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

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

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