Question

Factor 4x2 − 4x − 24 completely

Answer 1

Answer:

4(x-3)(x+2)

Step-by-step explanation:

Begin by dividing each term by 4.

$4x^2-4x-24 = 4(x^2-x-6)$

We now have a trinomial with a constant out front. Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial $ax^2+bx+c$ multiply a*c then find two numbers which multiply to this number and add to b. When you find those numbers, write them as $(x-/+ number)(x-/+number)$.

1. $x^2-x-6$

a=1, c=-6

ac=-6 and add to b=-1 which -3 and 2 satisfy.

Factors: (x-3)(x+2)

Place the 4 in front again and you have 4(x-3)(x+2).