Question

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

Answer 1

`(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)`

Answer 2

`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)`