Algebra Examples

$\frac{16 x^{5} - 48 x^{4} - 8 x^{3}}{8 x^{2}}$

Step 1

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

$8 x^{2}$

$0 x$

$0$

$16 x^{5}$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

$0 x$

$0$

Step 2

Divide the highest order term in the dividend $16 x^{5}$ by the highest order term in divisor $8 x^{2}$ .

$2 x^{3}$

$8 x^{2}$

$0 x$

$0$

$16 x^{5}$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

$0 x$

$0$

Step 3

Multiply the new quotient term by the divisor.

$2 x^{3}$

$8 x^{2}$

$0 x$

$0$

$16 x^{5}$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

$0 x$

$0$

$16 x^{5}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $16 x^{5} + 0 + 0$

$2 x^{3}$

$8 x^{2}$

$0 x$

$0$

$16 x^{5}$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

$0 x$

$0$

$16 x^{5}$

$0$

Step 5

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

						$2 x^{3}$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$

Step 6

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

$2 x^{3}$

$8 x^{2}$

$0 x$

$0$

$16 x^{5}$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

$0 x$

$0$

$16 x^{5}$

$0$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

Step 7

Divide the highest order term in the dividend $- 48 x^{4}$ by the highest order term in divisor $8 x^{2}$ .

$2 x^{3}$

$6 x^{2}$

$8 x^{2}$

$0 x$

$0$

$16 x^{5}$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

$0 x$

$0$

$16 x^{5}$

$0$

$48 x^{4}$

$8 x^{3}$

$0 x^{2}$

Step 8

Multiply the new quotient term by the divisor.

						$2 x^{3}$	-	$6 x^{2}$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							-	$48 x^{4}$	+	$0$	+	$0$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 48 x^{4} + 0 + 0$

						$2 x^{3}$	-	$6 x^{2}$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$

Step 10

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

						$2 x^{3}$	-	$6 x^{2}$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$
									-	$8 x^{3}$	+	$0$

Step 11

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

						$2 x^{3}$	-	$6 x^{2}$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$
									-	$8 x^{3}$	+	$0$	+	$0 x$	+	$0$

Step 12

Divide the highest order term in the dividend $- 8 x^{3}$ by the highest order term in divisor $8 x^{2}$ .

						$2 x^{3}$	-	$6 x^{2}$	-	$x$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$
									-	$8 x^{3}$	+	$0$	+	$0 x$	+	$0$

Step 13

Multiply the new quotient term by the divisor.

						$2 x^{3}$	-	$6 x^{2}$	-	$x$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$
									-	$8 x^{3}$	+	$0$	+	$0 x$	+	$0$
									-	$8 x^{3}$	+	$0$	+	$0$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 x^{3} + 0 + 0$

						$2 x^{3}$	-	$6 x^{2}$	-	$x$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$
									-	$8 x^{3}$	+	$0$	+	$0 x$	+	$0$
									+	$8 x^{3}$	-	$0$	-	$0$

Step 15

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

						$2 x^{3}$	-	$6 x^{2}$	-	$x$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$
									-	$8 x^{3}$	+	$0$	+	$0 x$	+	$0$
									+	$8 x^{3}$	-	$0$	-	$0$
														$0$

Step 16

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

						$2 x^{3}$	-	$6 x^{2}$	-	$x$
$8 x^{2}$	+	$0 x$	+	$0$		$16 x^{5}$	-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$	+	$0 x$	+	$0$
					-	$16 x^{5}$	-	$0$	-	$0$
							-	$48 x^{4}$	-	$8 x^{3}$	+	$0 x^{2}$
							+	$48 x^{4}$	-	$0$	-	$0$
									-	$8 x^{3}$	+	$0$	+	$0 x$	+	$0$
									+	$8 x^{3}$	-	$0$	-	$0$
														$0$	+	$0$

Step 17

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

$2 x^{3} - 6 x^{2} - x$