Exercises 72 and 73: A basic fact of algebra states that c is a root of a polynomial ƒ if and only if ƒ(x) = (x − c)g(x) for some polynomial g. We say that c is a multiple root if ƒ(x) = (x − c)²h(x), where h is a polynomial.

Show that c is a multiple root of ƒ if and only if c is a root of both ƒ and ƒ'.