# How do you factor quadratic equations with a coefficient?

Dec 21, 2014

Good question .

basically what are asking me to factor is :

$a {x}^{2} + b x + c$

here is an eg.

4x^2 – 15x + 9.

First you need to make column like this

SUM = COEFFICIENT OF x =( -15)
product = (COEFFICIENT of x^2 $\cdot$ COEFFICIENT of constant)= 36
Now you have to find factors which have a sum of -15 and a product of 36

THE FACTORS ARE (-12), (-3)

So now what we do is split the middle term in the equation and factor it out

4x^2 – 12x– 3x +9.
4x(x – 3)–3 (x-3).

(4x–3 )(x – 3).

HENCE FACTORED

f(4x^2 – 15x + 9.) = (4x–3 )(x – 3)