Finite Math Examples

$\frac{6 x^{3} + 7 x^{2} - 26 x - 15}{2 x + 5}$

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$2 x$

$5$

$6 x^{3}$

$7 x^{2}$

$26 x$

$15$

Step 2

Divide the highest order term in the dividend $6 x^{3}$ by the highest order term in divisor $2 x$ .

					$3 x^{2}$
	$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$

Step 3

Multiply the new quotient term by the divisor.

				$3 x^{2}$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			+	$6 x^{3}$	+	$15 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $6 x^{3} + 15 x^{2}$

				$3 x^{2}$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$

Step 5

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

				$3 x^{2}$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$

Step 6

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

				$3 x^{2}$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$

Step 7

Divide the highest order term in the dividend $- 8 x^{2}$ by the highest order term in divisor $2 x$ .

				$3 x^{2}$	-	$4 x$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$

Step 8

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$4 x$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					-	$8 x^{2}$	-	$20 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 x^{2} - 20 x$

				$3 x^{2}$	-	$4 x$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					+	$8 x^{2}$	+	$20 x$

Step 10

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

				$3 x^{2}$	-	$4 x$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					+	$8 x^{2}$	+	$20 x$
							-	$6 x$

Step 11

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

				$3 x^{2}$	-	$4 x$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					+	$8 x^{2}$	+	$20 x$
							-	$6 x$	-	$15$

Step 12

Divide the highest order term in the dividend $- 6 x$ by the highest order term in divisor $2 x$ .

				$3 x^{2}$	-	$4 x$	-	$3$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					+	$8 x^{2}$	+	$20 x$
							-	$6 x$	-	$15$

Step 13

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$4 x$	-	$3$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					+	$8 x^{2}$	+	$20 x$
							-	$6 x$	-	$15$
							-	$6 x$	-	$15$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 x - 15$

				$3 x^{2}$	-	$4 x$	-	$3$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					+	$8 x^{2}$	+	$20 x$
							-	$6 x$	-	$15$
							+	$6 x$	+	$15$

Step 15

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

				$3 x^{2}$	-	$4 x$	-	$3$
$2 x$	+	$5$		$6 x^{3}$	+	$7 x^{2}$	-	$26 x$	-	$15$
			-	$6 x^{3}$	-	$15 x^{2}$
					-	$8 x^{2}$	-	$26 x$
					+	$8 x^{2}$	+	$20 x$
							-	$6 x$	-	$15$
							+	$6 x$	+	$15$
										$0$

Step 16

Since the remander is $0$ , the final answer is the quotient.

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