Factorize the quadratic polynomials by using the method of completing

1.	Factorize the quadratic polynomials by using the method of completing the square:4x2 – 12x + 5
Answer» We have, 4x² – 12x + 5 4(x² – 3x + 5/4) Coefficient of x² is unity. So, we add and subtract square of half of coefficient of x. 4(x² – 3x + 5/4) = 4 [x² – 3x + (3/2)² – (3/2)² + 5/4] (Adding and subtracting (3/2)²) = 4 [(x – 3/2)² – 1²] (Completing the square) By using the formula (a² – b²) = (a+b) (a-b) = 4 (x – 3/2 + 1) (x – 3/2 – 1) = 4 (x – 1/2) (x – 5/2) (by taking LCM) = 4 [(2x-1)/2] [(2x – 5)/2] = (2x – 5) (2x – 1)

Factorize the quadratic polynomials by using the method of completing the square:4x2 – 12x + 5

Answer»

We have,

4x² – 12x + 5

4(x² – 3x + 5/4)

Coefficient of x² is unity. So, we add and subtract square of half of coefficient of x.

4(x² – 3x + 5/4) = 4 [x² – 3x + (3/2)² – (3/2)² + 5/4] (Adding and subtracting (3/2)²)

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

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

= 4 (x – 3/2 + 1) (x – 3/2 – 1)

= 4 (x – 1/2) (x – 5/2) (by taking LCM)

= 4 [(2x-1)/2] [(2x – 5)/2]

= (2x – 5) (2x – 1)