Q. 2 C4.4( 16 Votes )

# Factorize the following polynomials.

(x^{2} – 6x)^{2} – 8(x^{2} – 6x + 8) – 64

Answer :

(x^{2} – 6x) ^{2} – 8(x^{2} – 6x + 8) – 64

⟹ (x^{2} – 6x) ^{2} – 8(x^{2} -6x) - 64 – 64

⟹ (x^{2} – 6x) ^{2} – 8(x^{2} -6x) – 128

Put (x^{2} -6x) = a

⟹ (a) ^{2} – 8(a) – 128

⟹ a^{2} – 8a – 128

⟹ a^{2} – 16a + 8a - 128

⟹ a (a-16) + 8(a – 16)

⟹ (a + 8) × (a-16)

⟹ But a = (x^{2} -6x)

⟹ ((x^{2} -6x) + 8) × ((x^{2} -6x) – 16)

⟹ (x^{2} -6x + 8) × (x^{2} -6x – 16)

⟹ (x^{2} -4x – 2x + 8) × (x^{2} -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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