Question

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

a² - 14a - 51

Answer 1

a² – 14a – 51

Coefficient of a² = 1

Therefore, we have

a² – 14a – 51 = a² – 14a + 7² – 7² – 51 (Therefore, adding and subtracting 7²)

= (a – 7)² – 10² (Completing the square)

= (a – 7 + 10) (9 – 7 – 10)

= (a + 3) (a – 17)