Q. 13

Factorize each of the following algebraic expressions:


Answer :

a2 – 3a – 54

In order to factorize the given expression, we find to find two numbers p and q such that:


p + q = -3, pq = -54


Clearly,


6 – 9 = - 3, 6 (-9) = -54


Therefore, split – 3a as 6a – 9a


Therefore,


a2 – 3a – 54 = a2 + 6a – 9a – 54


= (a - 9) (a + 6)


Therefore,


(a + 7) (a – 10) + 16 = (a – 9) (a + 6)


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