Factorize the quadratic polynomials by using the method of completing

1.	Factorize the quadratic polynomials by using the method of completing the square:4y2 + 12y + 5
Answer» We have, 4y² + 12y + 5 4(y² + 3y + 5/4) Coefficient of y² is unity. So, we add and subtract square of half of coefficient of y. 4(y² + 3y + 5/4) = 4 [y² + 3y + (3/2)² – (3/2)² + 5/4] (Adding and subtracting (3/2)²) = 4 [(y + 3/2)² – 1²] (Completing the square) By using the formula (a² – b²) = (a+b) (a-b) = 4 (y + 3/2 + 1) (y + 3/2 – 1) = 4 (y + 1/2) (y + 5/2) (by taking LCM) = 4 [(2y + 1)/2] [(2y + 5)/2] = (2y + 1) (2y + 5)

Factorize the quadratic polynomials by using the method of completing the square:4y2 + 12y + 5

Answer»

We have,

4y² + 12y + 5

4(y² + 3y + 5/4)

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

4(y² + 3y + 5/4) = 4 [y² + 3y + (3/2)² – (3/2)² + 5/4] (Adding and subtracting (3/2)²)

= 4 [(y + 3/2)² – 1²] (Completing the square)

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

= 4 (y + 3/2 + 1) (y + 3/2 – 1)

= 4 (y + 1/2) (y + 5/2) (by taking LCM)

= 4 [(2y + 1)/2] [(2y + 5)/2]

= (2y + 1) (2y + 5)