Question

How do you use the factor theorem to determine whether x+4 is a factor of `2x^3 + x^2 - 25x + 12`?

Answer 1

See below:

Explanation:

Let's say we have a function `f(x)`:

If `f(c)=0`, then `x-c` is a factor of `f(x)`.

We want to see if `x+4` is a factor, so we can essentially evaluate `f(-4)`. If we get zero, it is a factor. If we don't, it isn't.

Let's evaluate this function at `x=-4`:

`2(-4)^3+(-4)^2-25(-4)+12=0`

We do indeed get zero, which means `x+4` is a factor of our polynomial.

Hope this helps!