Factorize the quadratic polynomials by using the method of completing

1.	Factorize the quadratic polynomials by using the method of completing the square:y2 – 7y + 12
Answer» We have, y² – 7y + 12 Coefficient of y² is unity. So, we add and subtract square of half of coefficient of y. y² – 7y + 12 = y² – 7y + (7/2)² – (7/2)² + 12 [Adding and subtracting (7/2)²] = (y – 7/2)² – (7/2)² (Completing the square) By using the formula (a² – b²) = (a+b) (a-b) = (y – (7/2- 1/2)) (y – (7/2 + 1/2)) = (y – 3) (y – 4)

Factorize the quadratic polynomials by using the method of completing the square:y2 – 7y + 12

Answer»

We have,

y² – 7y + 12

Coefficient of y² is unity. So, we add and subtract square of half of coefficient of y.

y² – 7y + 12 = y² – 7y + (7/2)² – (7/2)² + 12 [Adding and subtracting (7/2)²]

= (y – 7/2)² – (7/2)² (Completing the square)

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

= (y – (7/2- 1/2)) (y – (7/2 + 1/2))

= (y – 3) (y – 4)