Question

Factorize : (x2– x )2–8 ( x2– x ) + 12​

Answer 1

Answer:

(x²-x)²-8(x²-x)+12

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

Step-by-step explanation:

(x²-x)²-8(x²-x)+12

Let x²-x = a, the expression becomes

a²-8a+12

Splitting the middle term, we get

= a²-6a-2a+12

= a(a-6)-2(a-6)

= (a-6)(a-2)

= (x²-x-6)(x²-x-2)

= (x²-3x+2x-6)(x²-2x+x-2)

= [x(x-3)+2(x-3)][x(x-2)+1(x-2)]

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

Therefore,

(x²-x)²-8(x²-x)+12

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

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