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.

#Algebra

Easy Math Editor

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Comments

That was helpful..... Thanks.

salmaan shahid - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$