Question

Factorize each of the following quadratic polynomials by using the method of completing:

q² - 10q + 21

Answer 1

q² – 10q + 21 Coefficient of q² is 1 so we add and subtract square of half of coefficient of q

Therefore,

q² – 10q + 21 = q² – 10q + 5² – 5² + 21 (Adding and subtracting 5²)

= (q – 5)² – 2² (By completing the square)

= (q – 5 – 2) (q – 5 + 2)

= (q – 7) (q – 3)