Factorize the quadratic polynomials by using the method of completing

1.	Factorize the quadratic polynomials by using the method of completing the square:p2 + 6p + 8
Answer» 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)

Factorize the quadratic polynomials by using the method of completing the square:p2 + 6p + 8

Answer»

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)