Question

Factorize the quadratic polynomials by using the method of completing the square:

z² – 4z – 12

Answer 1

We have,

z² – 4z – 12

Coefficient of z² is unity. So, we add and subtract square of half of coefficient of z.

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

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

By using the formula (a² – b²) = (a+b) (a-b)

= (z – 2 + 4) (z – 2 – 4)

= (z – 6) (z + 2)