Finite Math Examples

$\frac{100 x^{12} + 220 x^{11} - 4619 x^{10} - 11044 x^{9} + 57611 x^{8} + 171374 x^{7} - 55025 x^{6} - 82553 x^{5} - 1557191 x^{4} + 153786 x^{3} + 888084 x^{2} + 21600 x - 12960}{x - 5}$

Step 1

Place the numbers representing the divisor and the dividend into a division-like configuration.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$

Step 2

The first number in the dividend $(100)$ is put into the first position of the result area (below the horizontal line).

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$

	$100$

Step 3

Multiply the newest entry in the result $(100)$ by the divisor $(5)$ and place the result of $(500)$ under the next term in the dividend $(220)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$
	$100$

Step 4

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$
	$100$	$720$

Step 5

Multiply the newest entry in the result $(720)$ by the divisor $(5)$ and place the result of $(3600)$ under the next term in the dividend $(- 4619)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$
	$100$	$720$

Step 6

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$
	$100$	$720$	$- 1019$

Step 7

Multiply the newest entry in the result $(- 1019)$ by the divisor $(5)$ and place the result of $(- 5095)$ under the next term in the dividend $(- 11044)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$
	$100$	$720$	$- 1019$

Step 8

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$
	$100$	$720$	$- 1019$	$- 16139$

Step 9

Multiply the newest entry in the result $(- 16139)$ by the divisor $(5)$ and place the result of $(- 80695)$ under the next term in the dividend $(57611)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$
	$100$	$720$	$- 1019$	$- 16139$

Step 10

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$

Step 11

Multiply the newest entry in the result $(- 23084)$ by the divisor $(5)$ and place the result of $(- 115420)$ under the next term in the dividend $(171374)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$

Step 12

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$

Step 13

Multiply the newest entry in the result $(55954)$ by the divisor $(5)$ and place the result of $(279770)$ under the next term in the dividend $(- 55025)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$

Step 14

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$

Step 15

Multiply the newest entry in the result $(224745)$ by the divisor $(5)$ and place the result of $(1123725)$ under the next term in the dividend $(- 82553)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$

Step 16

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$

Step 17

Multiply the newest entry in the result $(1041172)$ by the divisor $(5)$ and place the result of $(5205860)$ under the next term in the dividend $(- 1557191)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$

Step 18

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$

Step 19

Multiply the newest entry in the result $(3648669)$ by the divisor $(5)$ and place the result of $(18243345)$ under the next term in the dividend $(153786)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$

Step 20

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$	$18397131$

Step 21

Multiply the newest entry in the result $(18397131)$ by the divisor $(5)$ and place the result of $(91985655)$ under the next term in the dividend $(888084)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$	$91985655$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$	$18397131$

Step 22

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$	$91985655$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$	$18397131$	$92873739$

Step 23

Multiply the newest entry in the result $(92873739)$ by the divisor $(5)$ and place the result of $(464368695)$ under the next term in the dividend $(21600)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$	$91985655$	$464368695$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$	$18397131$	$92873739$

Step 24

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$	$91985655$	$464368695$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$	$18397131$	$92873739$	$464390295$

Step 25

Multiply the newest entry in the result $(464390295)$ by the divisor $(5)$ and place the result of $(2321951475)$ under the next term in the dividend $(- 12960)$ .

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$	$91985655$	$464368695$	$2321951475$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$	$18397131$	$92873739$	$464390295$

Step 26

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$5$	$100$	$220$	$- 4619$	$- 11044$	$57611$	$171374$	$- 55025$	$- 82553$	$- 1557191$	$153786$	$888084$	$21600$	$- 12960$
		$500$	$3600$	$- 5095$	$- 80695$	$- 115420$	$279770$	$1123725$	$5205860$	$18243345$	$91985655$	$464368695$	$2321951475$
	$100$	$720$	$- 1019$	$- 16139$	$- 23084$	$55954$	$224745$	$1041172$	$3648669$	$18397131$	$92873739$	$464390295$	$2321938515$

Step 27

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$100 x^{11} + 720 x^{10} - 1019 x^{9} + - 16139 x^{8} - 23084 x^{7} + 55954 x^{6} + 224745 x^{5} + 1041172 x^{4} + 3648669 x^{3} + 18397131 x^{2} + (92873739) x + 464390295 + \frac{2321938515}{x - 5}$

Step 28

Simplify the quotient polynomial.

$100 x^{11} + 720 x^{10} - 1019 x^{9} - 16139 x^{8} - 23084 x^{7} + 55954 x^{6} + 224745 x^{5} + 1041172 x^{4} + 3648669 x^{3} + 18397131 x^{2} + 92873739 x + 464390295 + \frac{2321938515}{x - 5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$