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# The theorem

The Remainder-Factor Theorem tells us that:

Let p(x) be an $$n^{th}$$ degree polynomial. If $$p(x)$$ is divided by $$x-c$$, the residue (or remainder) left is $$p(c)$$.

Proof: $$p(x)$$ can be rewriten as $$(x-c)q(x) + r$$ when $$q(x)$$ is an $$(n-1)^{th}$$ degree polynomial and $$r$$ is the remainder. Thus $$p(c) = r$$. Hence, proved.

The Theorem can be applied to the following:

$$(x-c)|P(x) \leftrightarrow P(c) = 0$$

Sorry for ugly formatting. I hope at least you get the idea.

Note by Sanchayapol Lewgasamsarn
2 years, 7 months ago

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