Factorize the following polynomials: (x^2-x )^2-8 (x^2-x )+12 - Vidyadip

Question

Factorize the following polynomials: $\left(x^2-x\right)^2-8\left(x^2-x\right)+12$

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Answer

$\left(x^2-x\right)^2-8\left(x^2-x\right)+12$
$=m^2-8 m+12 \ldots\left[\text { Putting } x^2-x=m\right]$
$=m^2-6 m-2 m+12$
$=m(m-6)-2(m-6)$
$=(m-6)(m-2)$
$=\left(x^2-x-6\right)\left(x^2-x-2\right) \ldots\left[\text { Replacing } m=x^2-x\right]$
$=\left(x^2-3 x+2 x-6\right)\left(x^2-2 x+x-2\right)$
$=[x(x-3)+2(x-3)][x(x-2)+1(x-2)]$
$=(x-3)(x+2)(x-2)(x+1)$

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