Q. 2 A4.0( 17 Votes )

Factorize the following polynomials.

(x2 – x)2 – 8(x2 – x) + 12

Answer :

Put (x2 – x) = a

a2 – 8a + 12


a2 – 2a – 6a + 12


a (a-2) – 6(a-2)


(a-6) × (a-2)


but a = (x2 – x)


((x2 – x)-6) × ((x2 – x) – 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 + 2)(x-3)(x-2)(x+1)


Therefore, the factorized form = (x + 2)(x-3)(x-2)(x+1)


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