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.

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TopNewestThat was helpful..... Thanks. – Salmaan Shahid · 2 years ago

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