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Question

Factorize the following quadratic polynomial by using the method of completing the square:

a2+2a3

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Solution

Given: a2+2a3

Since, the coefficient of a2 is unity.

Adding and subtracting (12× coefficient of a)2

i.e., (1)2

a2+2a3

=a2+2a+12123

=(a2+2a+12)4

=(a+1)222

=(a+1+2)(a+12)

=(a+3)(a1)

Hence, a2+2a3=(a+3)(a1)

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