Finite Math Examples

$\frac{7 x^{2} - 4 x - 3}{x + 2}$

Step 1

To calculate the remainder, first divide the polynomials.

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Step 1.1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of

$0$ .

$x$

$2$

$7 x^{2}$

$4 x$

$3$

Step 1.2

Divide the highest order term in the dividend

$7 x^{2}$ by the highest order term in divisor

$x$ .

					$7 x$
	$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$

Step 1.3

Multiply the new quotient term by the divisor.

				$7 x$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			+	$7 x^{2}$	+	$14 x$

Step 1.4

The expression needs to be subtracted from the dividend, so change all the signs in

$7 x^{2} + 14 x$

				$7 x$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			-	$7 x^{2}$	-	$14 x$

Step 1.5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$7 x$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			-	$7 x^{2}$	-	$14 x$
					-	$18 x$

Step 1.6

Pull the next terms from the original dividend down into the current dividend.

				$7 x$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			-	$7 x^{2}$	-	$14 x$
					-	$18 x$	-	$3$

Step 1.7

Divide the highest order term in the dividend

$- 18 x$ by the highest order term in divisor

$x$ .

				$7 x$	-	$18$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			-	$7 x^{2}$	-	$14 x$
					-	$18 x$	-	$3$

Step 1.8

Multiply the new quotient term by the divisor.

				$7 x$	-	$18$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			-	$7 x^{2}$	-	$14 x$
					-	$18 x$	-	$3$
					-	$18 x$	-	$36$

Step 1.9

The expression needs to be subtracted from the dividend, so change all the signs in

$- 18 x - 36$

				$7 x$	-	$18$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			-	$7 x^{2}$	-	$14 x$
					-	$18 x$	-	$3$
					+	$18 x$	+	$36$

Step 1.10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$7 x$	-	$18$
$x$	+	$2$		$7 x^{2}$	-	$4 x$	-	$3$
			-	$7 x^{2}$	-	$14 x$
					-	$18 x$	-	$3$
					+	$18 x$	+	$36$
							+	$33$

Step 1.11

The final answer is the quotient plus the remainder over the divisor.

$7 x - 18 + \frac{33}{x + 2}$

Step 2

Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.

$33$

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