Đáp án+Giải thích các bước giải:
a,
$x^4-x^2+x-1$
$=x^2(x^2-1)+(x-1)$
$=x^2(x-1)(x+1)+(x-1)$
$=(x-1)(x^3+x^2+1)$
b,
$2x^2-5x-3$
$=2x^2-6x+x-3$
$=2x(x-3)+(x-3)$
$=(x-3)(2x+1)$
c,
$3x^2-5x-2$
$=3x^2-6x+x-2$
$=3x(x-2)+(x-2)$
$=(x-2)(3x+1)$
d,
$x^3+2x-3$
$=x^3-x^2+x^2-x+3x-3$
$=x^2(x-1)+x(x-1)+3(x-1)$
$=(x^2+x+3)(x-1)$
e,
$x^4-9x^3+28x^2-36x+16$
$=x^4-x^3-8x^3+8x^2+20x^2-20x-16x+16$
$=x^3(x-1)-8x^2(x-1)+20x(x-1)-16(x-1)$
$=(x-1)(x^3-8x^2+20x-16)$
$=(x-1)(x^3-2x^2-6x^2+12x+8x-16)$
$=(x-1)[x^2(x-2)-6x(x-2)+8(x-2)]$
$=(x-1)(x-2)(x^2-6x+8)$
$=(x-1)(x-2)(x^2-2x-4x+8)$
$=(x-1)(x-2)[x(x-2)-4(x-2)]$
$=(x-1)(x-2)^2(x-4)$