Q. 2 D3.8( 14 Votes )

Factorize the following polynomials.

(x2 – 2x + 3) (x2 – 2x + 5) – 35

Answer :

(x2 – 2x + 3) (x2 – 2x + 5) – 35

Put (x2 – 2x) = a


(a + 3) (a + 5) – 35


(a2 + 5a + 3a + 15) – 35


a2 + 8a + 15 – 35


a2 + 8a – 20


a2 + 10a – 2a – 20


a (a + 10) – 2 (a + 10)


(a – 2) (a + 10)


But a = (x2 – 2x)


(x2 – 2x) + 10) ((x2 – 2x) – 2)


(x2 – 2x + 10) (x2 – 2x – 2)


Therefore, the factorized form = (x2 – 2x + 10) (x2 – 2x – 2)


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