Finite Math Examples

$\frac{15 a^{4} - 5 a^{3} + 10}{5 a}$

Step 1

Divide each term in the denominator by

$5$ to make the coefficient of linear factor variable

$1$ .

$\frac{1}{5} \cdot \frac{15 a^{4} - 5 a^{3} + 10}{a}$

Step 2

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

$0$	$15$	$- 5$	$0$	$0$	$10$

Step 3

The first number in the dividend

$(15)$ is put into the first position of the result area (below the horizontal line).

$0$	$15$	$- 5$	$0$	$0$	$10$

	$15$

Step 4

Multiply the newest entry in the result

$(15)$ by the divisor

$(0)$ and place the result of

$(0)$ under the next term in the dividend

$(- 5)$ .

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$
	$15$

Step 5

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

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$
	$15$	$- 5$

Step 6

Multiply the newest entry in the result

$(- 5)$ by the divisor

$(0)$ and place the result of

$(0)$ under the next term in the dividend

$(0)$ .

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$	$0$
	$15$	$- 5$

Step 7

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

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$	$0$
	$15$	$- 5$	$0$

Step 8

Multiply the newest entry in the result

$(0)$ by the divisor

$(0)$ and place the result of

$(0)$ under the next term in the dividend

$(0)$ .

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$	$0$	$0$
	$15$	$- 5$	$0$

Step 9

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

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$	$0$	$0$
	$15$	$- 5$	$0$	$0$

Step 10

Multiply the newest entry in the result

$(0)$ by the divisor

$(0)$ and place the result of

$(0)$ under the next term in the dividend

$(10)$ .

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$	$0$	$0$	$0$
	$15$	$- 5$	$0$	$0$

Step 11

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

$0$	$15$	$- 5$	$0$	$0$	$10$
		$0$	$0$	$0$	$0$
	$15$	$- 5$	$0$	$0$	$10$

Step 12

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

$(\frac{1}{5}) \cdot (15 a^{3} + - 5 a^{2} + (0) a + 0 + \frac{10}{a})$

Step 13

Simplify the quotient polynomial.

$(\frac{1}{5}) \cdot (15 a^{3} - 5 a^{2} + \frac{10}{a})$

Step 14

Simplify.

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Step 14.1

Distribute.

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Step 14.1.1

Apply the distributive property.

$\frac{1}{5} \cdot (15 a^{3} - 5 a^{2}) + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.1.2

Apply the distributive property.

$\frac{1}{5} \cdot (15 a^{3}) + \frac{1}{5} \cdot (- 5 a^{2}) + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.2

Cancel the common factor of

$5$ .

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Step 14.2.1

Factor

$5$ out of

$15 a^{3}$ .

$\frac{1}{5} \cdot (5 (3 a^{3})) + \frac{1}{5} \cdot (- 5 a^{2}) + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.2.2

Cancel the common factor.

$\frac{1}{5} \cdot (5 (3 a^{3})) + \frac{1}{5} \cdot (- 5 a^{2}) + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.2.3

Rewrite the expression.

$3 a^{3} + \frac{1}{5} \cdot (- 5 a^{2}) + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.3

Cancel the common factor of

$5$ .

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Step 14.3.1

Factor

$5$ out of

$- 5 a^{2}$ .

$3 a^{3} + \frac{1}{5} \cdot (5 (- a^{2})) + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.3.2

Cancel the common factor.

$3 a^{3} + \frac{1}{5} \cdot (5 (- a^{2})) + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.3.3

Rewrite the expression.

$3 a^{3} - a^{2} + \frac{1}{5} \cdot \frac{10}{a}$

Step 14.4

Cancel the common factor of

$5$ .

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Step 14.4.1

Factor

$5$ out of

$10$ .

$3 a^{3} - a^{2} + \frac{1}{5} \cdot \frac{5 (2)}{a}$

Step 14.4.2

Cancel the common factor.

$3 a^{3} - a^{2} + \frac{1}{5} \cdot \frac{5 \cdot 2}{a}$

Step 14.4.3

Rewrite the expression.

$3 a^{3} - a^{2} + \frac{2}{a}$