Factorize the quadratic polynomials by using the method of completing

1.	Factorize the quadratic polynomials by using the method of completing the square:z2 – 4z – 12
Answer» 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)

Factorize the quadratic polynomials by using the method of completing the square:z2 – 4z – 12

Answer»

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)