Q. 2 E4.0( 21 Votes )

Factorize the following polynomials.

(y+2) (y+3) (y-3) (y + 8) + 56

Answer :

(y+2) (y+3) (y-3) (y + 8) + 56

(y2 + 3y + 2y + 6) (y2 + 8y - 3y - 24) + 5


(y2 + 5y + 6) (y2 + 5y - 24) + 56


Put (y2 + 5y) = a


(a + 6) (a – 24) + 56


a2 -24a + 6a – 144 + 56


a2 – 18a – 88


a2 -22a + 4a – 88


a (a-22) + 4 (a-22)


(a+4) (a-22)


But a = (y2 + 5y)


((y2 + 5y) + 4) ((y2 + 5y)-22)


(y2 + 5y + 4) (y2 + 5y -22)


(y2 + 4y + y + 4) (y2 + 5y -22)


(y (y+4) + 1(y+4)) (y2 + 5y -22)


(y+1) (y+ 4) (y2 + 5y -22)


Therefore, the factorized form = (y+1) (y+ 4) (y2 + 5y -22)


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