Finite Math Examples

$\frac{4 x^{3} - 19 x^{2} - 58 x - 35}{4 x + 5}$

Step 1

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

$4 x$

$5$

$4 x^{3}$

$19 x^{2}$

$58 x$

$35$

Step 2

Divide the highest order term in the dividend $4 x^{3}$ by the highest order term in divisor $4 x$ .

					$x^{2}$
	$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$

Step 3

Multiply the new quotient term by the divisor.

				$x^{2}$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			+	$4 x^{3}$	+	$5 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{3} + 5 x^{2}$

				$x^{2}$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$

Step 5

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

				$x^{2}$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$

Step 6

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

				$x^{2}$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$

Step 7

Divide the highest order term in the dividend $- 24 x^{2}$ by the highest order term in divisor $4 x$ .

				$x^{2}$	-	$6 x$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$

Step 8

Multiply the new quotient term by the divisor.

				$x^{2}$	-	$6 x$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					-	$24 x^{2}$	-	$30 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 24 x^{2} - 30 x$

				$x^{2}$	-	$6 x$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					+	$24 x^{2}$	+	$30 x$

Step 10

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

				$x^{2}$	-	$6 x$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					+	$24 x^{2}$	+	$30 x$
							-	$28 x$

Step 11

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

				$x^{2}$	-	$6 x$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					+	$24 x^{2}$	+	$30 x$
							-	$28 x$	-	$35$

Step 12

Divide the highest order term in the dividend $- 28 x$ by the highest order term in divisor $4 x$ .

				$x^{2}$	-	$6 x$	-	$7$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					+	$24 x^{2}$	+	$30 x$
							-	$28 x$	-	$35$

Step 13

Multiply the new quotient term by the divisor.

				$x^{2}$	-	$6 x$	-	$7$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					+	$24 x^{2}$	+	$30 x$
							-	$28 x$	-	$35$
							-	$28 x$	-	$35$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 28 x - 35$

				$x^{2}$	-	$6 x$	-	$7$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					+	$24 x^{2}$	+	$30 x$
							-	$28 x$	-	$35$
							+	$28 x$	+	$35$

Step 15

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

				$x^{2}$	-	$6 x$	-	$7$
$4 x$	+	$5$		$4 x^{3}$	-	$19 x^{2}$	-	$58 x$	-	$35$
			-	$4 x^{3}$	-	$5 x^{2}$
					-	$24 x^{2}$	-	$58 x$
					+	$24 x^{2}$	+	$30 x$
							-	$28 x$	-	$35$
							+	$28 x$	+	$35$
										$0$

Step 16

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

$x^{2} - 6 x - 7$