Q. 2 C4.4( 16 Votes )

Factorize the following polynomials.

(x2 – 6x)2 – 8(x2 – 6x + 8) – 64

Answer :

(x2 – 6x) 2 – 8(x2 – 6x + 8) – 64

(x2 – 6x) 2 – 8(x2 -6x) - 64 – 64


(x2 – 6x) 2 – 8(x2 -6x) – 128


Put (x2 -6x) = a


(a) 2 – 8(a) – 128


a2 – 8a – 128


a2 – 16a + 8a - 128


a (a-16) + 8(a – 16)


(a + 8) × (a-16)


But a = (x2 -6x)


((x2 -6x) + 8) × ((x2 -6x) – 16)


(x2 -6x + 8) × (x2 -6x – 16)


(x2 -4x – 2x + 8) × (x2 -8x + 2x – 16)


(x(x-4) – 2(x-4)) × (x(x-8) + 2(x-8)


(x-2)(x-4)(x-8)(x+2)


Therefore, the factorized form = (x-2) (x-4) (x-8) (x+2)


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