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### High School Mathematics - 212.9 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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