Question

Factorize each of the following quadratic polynomials by using the method of completing:

4y² + 12y + 5

Answer 1

4y² + 12y + 5

We have 4y² + 12y + 5 = 4 (y² + 3y + \(\frac{5}{4}\)) [Therefore, coefficient of y² = 1]

= 4 [y² + 3y + (\(\frac{3}{2}\))² – (\(\frac{3}{2}\))² + \(\frac{5}{4}\)]

= 4 [(y + \(\frac{3}{2}\))² – 1²] (Completing the square)

= 4 (y + \(\frac{3}{2}\) + 1) (y + \(\frac{3}{2}\) – 1)

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