Question

Can someone explain The Factor Theorem and The Remainder Theorem to me?

Answer 1

I've already read an article by "Math is Fun" and "Purple Math," but I can't seem to wrap my head around the concept.

Answer 2

When you divide a polynomial f(x) by x-c you get:

f(x) = (x-c)·q(x) + r(x)

But r(x) is simply the constant r (remember? when you divide by (x-c) the remainder is a constant) .... so you get this:

f(x) = (x-c)·q(x) + r

Now see what happens when x is equal to c:

f(c) = (c-c)·q(c) + r

f(c) = (0)·q(c) + r

f(c) = r

Answer 3

What does each of those terms mean? What is "x-c" what do the variables represent in this sense?