Finite Math Examples

$\frac{8 x^{3} - 14 x^{2} - 19 x - 3}{4 x + 3}$

Step 1

Divide each term in the denominator by $4$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{4} \cdot \frac{8 x^{3} - 14 x^{2} - 19 x - 3}{\frac{4 x + 3}{4}}$

Step 2

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

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$

Step 3

The first number in the dividend $(8)$ is put into the first position of the result area (below the horizontal line).

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$

	$8$

Step 4

Multiply the newest entry in the result $(8)$ by the divisor $(- \frac{3}{4})$ and place the result of $(- 6)$ under the next term in the dividend $(- 14)$ .

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$
		$- 6$
	$8$

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.

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$
		$- 6$
	$8$	$- 20$

Step 6

Multiply the newest entry in the result $(- 20)$ by the divisor $(- \frac{3}{4})$ and place the result of $(15)$ under the next term in the dividend $(- 19)$ .

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$
		$- 6$	$15$
	$8$	$- 20$

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.

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$
		$- 6$	$15$
	$8$	$- 20$	$- 4$

Step 8

Multiply the newest entry in the result $(- 4)$ by the divisor $(- \frac{3}{4})$ and place the result of $(3)$ under the next term in the dividend $(- 3)$ .

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$
		$- 6$	$15$	$3$
	$8$	$- 20$	$- 4$

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.

$- \frac{3}{4}$	$8$	$- 14$	$- 19$	$- 3$
		$- 6$	$15$	$3$
	$8$	$- 20$	$- 4$	$0$

Step 10

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

$(\frac{1}{4}) \cdot (8 x^{2} + - 20 x - 4)$

Step 11

Simplify the quotient polynomial.

$(\frac{1}{4}) \cdot (8 x^{2} - 20 x - 4)$

Step 12

Simplify.

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Step 12.1

Distribute.

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Step 12.1.1

Apply the distributive property.

$\frac{1}{4} \cdot (8 x^{2} - 20 x) + \frac{1}{4} \cdot - 4$

Step 12.1.2

Apply the distributive property.

$\frac{1}{4} \cdot (8 x^{2}) + \frac{1}{4} \cdot (- 20 x) + \frac{1}{4} \cdot - 4$

Step 12.2

Cancel the common factor of $4$ .

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Step 12.2.1

Factor $4$ out of $8 x^{2}$ .

$\frac{1}{4} \cdot (4 (2 x^{2})) + \frac{1}{4} \cdot (- 20 x) + \frac{1}{4} \cdot - 4$

Step 12.2.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 (2 x^{2})) + \frac{1}{4} \cdot (- 20 x) + \frac{1}{4} \cdot - 4$

Step 12.2.3

Rewrite the expression.

$2 x^{2} + \frac{1}{4} \cdot (- 20 x) + \frac{1}{4} \cdot - 4$

Step 12.3

Cancel the common factor of $4$ .

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Step 12.3.1

Factor $4$ out of $- 20 x$ .

$2 x^{2} + \frac{1}{4} \cdot (4 (- 5 x)) + \frac{1}{4} \cdot - 4$

Step 12.3.2

Cancel the common factor.

$2 x^{2} + \frac{1}{4} \cdot (4 (- 5 x)) + \frac{1}{4} \cdot - 4$

Step 12.3.3

Rewrite the expression.

$2 x^{2} - 5 x + \frac{1}{4} \cdot - 4$

Step 12.4

Cancel the common factor of $4$ .

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Step 12.4.1

Factor $4$ out of $- 4$ .

$2 x^{2} - 5 x + \frac{1}{4} \cdot (4 (- 1))$

Step 12.4.2

Cancel the common factor.

$2 x^{2} - 5 x + \frac{1}{4} \cdot (4 \cdot - 1)$

Step 12.4.3

Rewrite the expression.

$2 x^{2} - 5 x - 1$