Q. 2 G4.3( 17 Votes )

# Factorize the following polynomials.

(x – 3) (x- 5) (x – 4)^{2} – 6

Answer :

(x – 3) (x- 5) (x – 4)^{2} – 6

⟹ (x^{2} – 8x + 15) (x^{2} – 8x + 16) – 6

⟹ Put (x^{2} – 8x) = a

⟹ (a + 15) (a + 16) – 6

⟹ a^{2} + 15a + 16a + 240 – 6

⟹ a^{2} + 31a + 234

⟹ a^{2} + 13a + 18a + 234

⟹ a (a + 13) + 18 (a + 13)

⟹ (a + 18) (a + 13)

⟹ But a = (x^{2} – 8x)

⟹ ((x^{2} – 8x) + 18) ((x^{2} – 8x) + 13)

⟹ (x^{2} – 8x + 18) (x^{2} – 8x + 13)

Therefore, the factorized form =(x^{2} – 8x + 18) (x^{2} – 8x + 13)

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