How do you factor quadratic equations with a coefficient?

1 Answer
Sidharth · Steve M
Dec 21, 2014

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)#

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