Question

(3) Factorize the following polynomial

$( x {}^{2} - x) {}^{2} - 8(x {}^{2} - x) + 12$
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Answer 1

Step-by-step explanation:

let (x^2-x)=y

y^2-8y+12=0

y^2-6y-2y+12=0

y(y-6)-2(y-6)=0

(y-2)(y-6)=0

y=2,y=6

when y=2

x^2-x=2

x^2-x-2=0

x^2-2x+x-2=0

x(x-2)+1(x-2)=0

(x+1) (x-2)=0

x=-1,x=2

When y=6

x^2-x-6=0

x^2-3x+2x-6=0

x(x-3)+2(x-3)=0

(x-3) (x+2)

x=3,x=-2

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