Finite Math Examples

$\frac{x^{4} + 3 x^{3} + 24 x^{2} + 192 x - 2560}{x^{2} + 64}$

Step 1

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

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

Step 2

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

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

Step 3

Multiply the new quotient term by the divisor.

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $x^{4} + 0 + 64 x^{2}$

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

Step 5

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

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

$3 x^{3}$

$40 x^{2}$

Step 6

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

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

$3 x^{3}$

$40 x^{2}$

$192 x$

Step 7

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

$x^{2}$

$3 x$

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

$3 x^{3}$

$40 x^{2}$

$192 x$

Step 8

Multiply the new quotient term by the divisor.

$x^{2}$

$3 x$

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

$3 x^{3}$

$40 x^{2}$

$192 x$

$3 x^{3}$

$0$

$192 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $3 x^{3} + 0 + 192 x$

$x^{2}$

$3 x$

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

$3 x^{3}$

$40 x^{2}$

$192 x$

$3 x^{3}$

$0$

$192 x$

Step 10

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

$x^{2}$

$3 x$

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

$3 x^{3}$

$40 x^{2}$

$192 x$

$3 x^{3}$

$0$

$192 x$

$40 x^{2}$

$0$

Step 11

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

$x^{2}$

$3 x$

$x^{2}$

$0 x$

$64$

$x^{4}$

$3 x^{3}$

$24 x^{2}$

$192 x$

$2560$

$x^{4}$

$0$

$64 x^{2}$

$3 x^{3}$

$40 x^{2}$

$192 x$

$3 x^{3}$

$0$

$192 x$

$40 x^{2}$

$0$

$2560$

Step 12

Divide the highest order term in the dividend $- 40 x^{2}$ by the highest order term in divisor $x^{2}$ .

						$x^{2}$	+	$3 x$	-	$40$
$x^{2}$	+	$0 x$	+	$64$		$x^{4}$	+	$3 x^{3}$	+	$24 x^{2}$	+	$192 x$	-	$2560$
					-	$x^{4}$	-	$0$	-	$64 x^{2}$
							+	$3 x^{3}$	-	$40 x^{2}$	+	$192 x$
							-	$3 x^{3}$	-	$0$	-	$192 x$
									-	$40 x^{2}$	+	$0$	-	$2560$

Step 13

Multiply the new quotient term by the divisor.

						$x^{2}$	+	$3 x$	-	$40$
$x^{2}$	+	$0 x$	+	$64$		$x^{4}$	+	$3 x^{3}$	+	$24 x^{2}$	+	$192 x$	-	$2560$
					-	$x^{4}$	-	$0$	-	$64 x^{2}$
							+	$3 x^{3}$	-	$40 x^{2}$	+	$192 x$
							-	$3 x^{3}$	-	$0$	-	$192 x$
									-	$40 x^{2}$	+	$0$	-	$2560$
									-	$40 x^{2}$	+	$0$	-	$2560$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 40 x^{2} + 0 - 2560$

						$x^{2}$	+	$3 x$	-	$40$
$x^{2}$	+	$0 x$	+	$64$		$x^{4}$	+	$3 x^{3}$	+	$24 x^{2}$	+	$192 x$	-	$2560$
					-	$x^{4}$	-	$0$	-	$64 x^{2}$
							+	$3 x^{3}$	-	$40 x^{2}$	+	$192 x$
							-	$3 x^{3}$	-	$0$	-	$192 x$
									-	$40 x^{2}$	+	$0$	-	$2560$
									+	$40 x^{2}$	-	$0$	+	$2560$

Step 15

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

						$x^{2}$	+	$3 x$	-	$40$
$x^{2}$	+	$0 x$	+	$64$		$x^{4}$	+	$3 x^{3}$	+	$24 x^{2}$	+	$192 x$	-	$2560$
					-	$x^{4}$	-	$0$	-	$64 x^{2}$
							+	$3 x^{3}$	-	$40 x^{2}$	+	$192 x$
							-	$3 x^{3}$	-	$0$	-	$192 x$
									-	$40 x^{2}$	+	$0$	-	$2560$
									+	$40 x^{2}$	-	$0$	+	$2560$
														$0$

Step 16

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

$x^{2} + 3 x - 40$