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

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

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

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