Question

How do you factor `x^ { 2} + 23x = 108`?

Answer 1

The factored form is `(x-4)(x+27)=0`.

Explanation:

First, move everything over to one side:

`x^2+23x=108`

`x^2+23x-108=0`

Now, find two numbers that multiply to `-108` and add to `23`.

These two numbers are `27` and `-4`. Split the `x` terms into these numbers, then factor the first two terms and last two terms separately, then combine them.

Here's what that looks like:

`x^2+27x-4x-108=0`

`color(red)x(x+27)-4x-108=0`

`color(red)x(x+27)color(blue)-color(blue)4(x+27)=0`

`(color(red)xcolor(blue)-color(blue)4)(x+27)=0`

This is the factored form. Hope this helped!