Hello, rlarach!

Prove that: . for all real numbers and

Let

I used the Factor Theorem a few times.

If , the polynomial has value 0.

. . Hence, is a factor of

Using long division: .

And we find that is a factor of the cubic.

Long division: .

. . Hence, we have: .

We see that:

. . and that: .

Therefore, for all real