factor this expression completely 14x^2 + 30x + 4

Question

by completing the square

Answer 1

Completing the square Method :

The expression is 14x² + 30x + 4.

Take out common factor.

= 14(x² + 15x/7 + 2/7)

To change the expression (x² + 15x/7) into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 15/7. So, (half the x coefficient)² = (15/14)² = 225/196.

Add and subtract 225/196 to the expression.

= 14(x² + 15x/7 + 225/196 - 225/196 + 2/7)

= 14[{x² + 2(15/14)x + (15/14)²} - (225/196 - 2/7)]

= 14[{x² + 2(15/14)x + (15/14)²} - (225 - 56)/196]

Apply Perfect Square Trinomial : u² + 2uv + v² = (u + v)².

= 14[(x + 15/14)² - (169/196)]

= 14[(x + 15/14)² - (13/14)²]

Apply Difference of Two Squares : u² - v² = (u + v)(u - v).

= 14(x + 15/14 + 13/14)(x + 15/14 - 13/14)

= 14(x + 2)(x + 2/14)

= (x + 2)(14x + 2)

The factorization form of the expression is (x + 2)(14x + 2).