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Question

Factorize each of the following quadratic polynomials by using the method of completing the square:
q2 − 10q + 21

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Solution

q2-10q+21=q2-10q+1022-1022+21 [Adding and subtracting 1022, that is, 52]=q2-2×q×5+52-52+21=(q-5)2-4 [Completing the square]=(q-5)2-22 =[(q-5)-2][(q-5)+2]=(q-5-2)(q-5+2)=(q-7)(q-3)

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