Factorize the quadratic polynomials by using the method of completing

1.	Factorize the quadratic polynomials by using the method of completing the square:q2 – 10q + 21
Answer» We have, q² – 10q + 21 Coefficient of q² is unity. So, we add and subtract square of half of coefficient of q. q² – 10q + 21 = q² – 10q+ 5² – 5² + 21 (Adding and subtracting 5²) = (q – 5)² – 2² (By completing the square) By using the formula (a² – b²) = (a+b) (a-b) = (q – 5 – 2) (q – 5 + 2) = (q – 3) (q – 7)

Factorize the quadratic polynomials by using the method of completing the square:q2 – 10q + 21

Answer»

We have,

q² – 10q + 21

Coefficient of q² is unity. So, we add and subtract square of half of coefficient of q.

q² – 10q + 21 = q² – 10q+ 5² – 5² + 21 (Adding and subtracting 5²)

= (q – 5)² – 2² (By completing the square)

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

= (q – 5 – 2) (q – 5 + 2)

= (q – 3) (q – 7)