Question

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

p² + 6p + 8

Answer 1

We have,

p² + 6p + 8

Coefficient of p² is unity. So, we add and subtract square of half of coefficient of p.

p² + 6p + 8 = p² + 6p + 3² – 3² + 8 (Adding and subtracting 3²)

= (p + 3)² – 1² (By completing the square)

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

= (p + 3 – 1) (p + 3 + 1)

= (p + 2) (p + 4)