How do you factor 24x ^ { 3} + 60x ^ { 2} - 168x - 420?

2 Answers
Jun 22, 2017

(12x^2-84)(2x+5)

Explanation:

Let's start with what we got:

24x^3+60x^2-168x-420

What we can do is break it up into:

24x^3+60x^2 & -168x-420

We will factor this by grouping, find the GCF for each of them:

The GCF for 24x^3+60x^2 is color(blue)(12x^2)

The GCF for -168x-420 is color(blue)(-42)

Now let's factor them:

24x^3+60x^2->color(blue)(12x^2)(2x+5)
-168x-420->color(blue)(-84)(2x+5)

We can see that color(blue)(12x^2)color(blue)(-84) is one factor the other one is 2x+5

Our final answer is (12x^2-84)(2x+5)

Jun 22, 2017

2(2x + 5)(2x^2 - 7)

Explanation:

f(x) = 12(2x^3 + 5x^2 - 14x - 35) = 12y
Factor y by grouping:
y = 2x^2(x + 5) - 7(2x + 5) = (2x + 5)(2x^2 - 7)
f(x) = 12(2x + 5)(2x^2 - 7)