Factorize the quadratic polynomials by using the method of completing

1.	Factorize the quadratic polynomials by using the method of completing the square:a2 + 2a – 3
Answer» We have, a² + 2a – 3 Coefficient of a² is unity. So, we add and subtract square of half of coefficient of a. a² + 2a – 3 = a² + 2a + 1² – 1² – 3 (Adding and subtracting 1²) = (a + 1)² – 2² (Completing the square) By using the formula (a² – b²) = (a+b) (a-b) = (a + 1 + 2) (a + 1 – 2) = (a + 3) (a – 1)

Factorize the quadratic polynomials by using the method of completing the square:a2 + 2a – 3

Answer»

We have,

a² + 2a – 3

Coefficient of a² is unity. So, we add and subtract square of half of coefficient of a.

a² + 2a – 3 = a² + 2a + 1² – 1² – 3 (Adding and subtracting 1²)

= (a + 1)² – 2² (Completing the square)

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

= (a + 1 + 2) (a + 1 – 2)

= (a + 3) (a – 1)