Remainder Theorem

The Remainder theorem formula is used to find the remainder when a polynomial is divided by a linear polynomial.

Remainder Theorem

The Remainder theorem states that "when a polynomial $p(x)$is divided by a linear polynomial $(x-a)$ , then the remainder is $p(a)$"

Example

Find the remainder when the polynomial $p(x)=x^{4}+2x^{3}-4x-3$ is divided by $(x-3)$.

	$3x^{2}-2x+4$
$x+1$	$3x^{3}$	$+$	$x^{2}$	$+$	$2x$	$+$	$5$
	$3x^{3}$	$+$	$3x^{2}$
		$-$	$2x^{2}$	$+$	$2x$	$+$	$5$
		$-$	$2x^{2}$	$-$	$2x$
				$+$	$4x$	$+$	$5$
				$+$	$4x$	$+$	$4$
							1