Question

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

z² - 4z - 12

Answer 1

z² – 4z – 12

Coefficient of z² = 1

Therefore, we have

z² – 4z – 12 = z² – 4z + 2² – 2² – 12 [By adding and subtracting 2²]

= (z – 2)² – 4² (Completing the square)

= (z – 2 + 4) (z – 2 – 4)

= (z + 2) (z – 6)