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High School Mathematics - 2
12.9 Factor Theorem

Statement: If p(x) is a ploynomial in x, divided by x-a and the remainder = f(a) is zero, then (x-a) is a factor of p(x).
Proof: When p(x) is divided by (x-a)
R = p(a) (by remainder theorem)
p(x) = (x-a) q(x) + p(a)
From remainder theorem we have
(x-a) is a factor of p(a)
Conversely if x-a is a factor of p(x) then p(a) = 0
p(x) = (x-a) q(x) + R
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