Question

Factorize the following polynomials.
$(x^2-x{)}^2-8(x^2-x)+12$

Answer 1

The polynomial is

${(x^2-x)}^2-8(x^2-x)+12$

$y=(x^2-x)$

Then the polynomial becomes,

$y^2-8y+12$

$=y^2-6y-2y+12$

$=y(y-6)-2(y-6)$

$=(y-2)(y-6)$

$=(x^2-x-2)(x^2-x-6)$

Now both factors can be further factorized,

$(x^2-2x+x-2)(x^2-3x+2x-6)$

$=\left\{x\right(x-2)+1(x-2\left)\right\}\left\{x\right(x-3)+2(x-3\left)\right\}$

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