How do you factor quadratic equations with a coefficient?

Good question .

basically what are asking me to factor is :

##ax^2 + bx +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 ##*## 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)##