Question

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

x² + 12x + 20

Answer 1

x² + 12x + 20

Coefficient of x² = 1

Therefore, we have

x² + 12x + 6² – 6² + 20 (Adding and subtracting 6²)

= (x + 6)² – 4² (Completing the square)

= (x + 6 + 4) (x + 6 – 4)

= (x + 10) (x + 2)

= 4 [x - \(\frac{3}{2}\) + 1] [x - \(\frac{3}{2}\) – 1]

= (2x – 1) (2x – 5)