Polynomial Remainder Theorem

Statement

The Polynomial Remainder Theorem states that for $\frac{f(x)}{x-a}$ the remainder is $f(a)$

Proof

Assuming $r$ = remainder $q(x)$ = quotient and $f(x)$ as a polynomial:

$f(x)=q(x)(x-a)+r$

If we plug in $a$ into the polynomial $f(x)$ and $x-a$ (Do not plug $a$ into $q(x)$. Assume $q(x)$ as only a variable for quotient) we get:

$f(a)=r$

See Also

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