Question

How do you factor `x^3-13x^2-30x` completely?

Answer 1

`x^3-13x^2-30x=color(blue)(x(x+2)(x-15)`

Explanation:

Factor:

`x^3-13x^2-30x`

Factor out the GCF `x`.

`x(x^2-13x-30)`

Factor `x^2-13x-30`

Find two numbers that when added equal `-13` and when multiplied equal `-30`. The numbers `2` and `-15` meet the requirements.

Rewrite the expression.

`x(x+2)(x-15)`

Answer 2

`x(x-15)(x+2)`

Explanation:

All terms have an `x` in common, so we can factor that out first. We get

`xcolor(blue)((x^2-13x-30))`

What I have in blue, I can factor by grouping. Here, I will rewrite the `b` term as the sum of two terms, so we can factor easily.

Our polynomial can be alternatively written as

`x(x^2+color(red)(2x-15x)-30)`

Notice, the red terms are the same as `-13x`, so I didn't change the value of this expression.

`x(color(purple)(x^2+2x)color(lime)(-15x-30))`

I can factor an `x` out of the purple term, and a `-15` out of the green term. Doing this, we get

`x(color(purple)(x(x+2))color(lime)(-15(x+2)))`

Both the green and purple terms have an `x+2` in common, so I can factor that out. We get

`x(color(purple)xcolor(lime)(-15))(x+2)`

as our final answer.

Hope this helps!