Question

How do you show that x+7 is a factor of `x^3-37x+84`. Then factor completely?

Answer 1

The completely factored form is `(x+7)(x-3)(x-4)`.

Explanation:

You can use synthetic division. I'm not going to explain how to do synthetic division here, but this website has a really good explanation of how it works.

Now we have our polynomial as `(x+7)(x^2-7x+12)`.

We can factor our quadratic using `-3` and `-4`:

`color(white)=(x+7)(x^2-7x+12)`

`=(x+7)(x^2-3x-4x+12)`

`=(x+7)((x-3)(x-4))`

`=(x+7)(x-3)(x-4)`

This is the fully factored polynomial. Hope this helped!