Finite Math Examples

$\frac{12 x^{3} - 20 x^{2} + x + 3}{2 x - 3}$

Step 1

Divide each term in the denominator by

$2$ to make the coefficient of linear factor variable

$1$ .

$\frac{1}{2} \cdot \frac{12 x^{3} - 20 x^{2} + x + 3}{\frac{2 x - 3}{2}}$

Step 2

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

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$

Step 3

The first number in the dividend

$(12)$ is put into the first position of the result area (below the horizontal line).

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$

	$12$

Step 4

Multiply the newest entry in the result

$(12)$ by the divisor

$(\frac{3}{2})$ and place the result of

$(18)$ under the next term in the dividend

$(- 20)$ .

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$
		$18$
	$12$

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.

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$
		$18$
	$12$	$- 2$

Step 6

Multiply the newest entry in the result

$(- 2)$ by the divisor

$(\frac{3}{2})$ and place the result of

$(- 3)$ under the next term in the dividend

$(1)$ .

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$
		$18$	$- 3$
	$12$	$- 2$

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.

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$
		$18$	$- 3$
	$12$	$- 2$	$- 2$

Step 8

Multiply the newest entry in the result

$(- 2)$ by the divisor

$(\frac{3}{2})$ and place the result of

$(- 3)$ under the next term in the dividend

$(3)$ .

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$
		$18$	$- 3$	$- 3$
	$12$	$- 2$	$- 2$

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.

$\frac{3}{2}$	$12$	$- 20$	$1$	$3$
		$18$	$- 3$	$- 3$
	$12$	$- 2$	$- 2$	$0$

Step 10

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

$(\frac{1}{2}) \cdot (12 x^{2} + - 2 x - 2)$

Step 11

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (12 x^{2} - 2 x - 2)$

Step 12

Simplify.

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Step 12.1

Distribute.

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Step 12.1.1

Apply the distributive property.

$\frac{1}{2} \cdot (12 x^{2} - 2 x) + \frac{1}{2} \cdot - 2$

Step 12.1.2

Apply the distributive property.

$\frac{1}{2} \cdot (12 x^{2}) + \frac{1}{2} \cdot (- 2 x) + \frac{1}{2} \cdot - 2$

Step 12.2

Cancel the common factor of

$2$ .

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Step 12.2.1

Factor

$2$ out of

$12 x^{2}$ .

$\frac{1}{2} \cdot (2 (6 x^{2})) + \frac{1}{2} \cdot (- 2 x) + \frac{1}{2} \cdot - 2$

Step 12.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 (6 x^{2})) + \frac{1}{2} \cdot (- 2 x) + \frac{1}{2} \cdot - 2$

Step 12.2.3

Rewrite the expression.

$6 x^{2} + \frac{1}{2} \cdot (- 2 x) + \frac{1}{2} \cdot - 2$

Step 12.3

Cancel the common factor of

$2$ .

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Step 12.3.1

Factor

$2$ out of

$- 2 x$ .

$6 x^{2} + \frac{1}{2} \cdot (2 (- x)) + \frac{1}{2} \cdot - 2$

Step 12.3.2

Cancel the common factor.

$6 x^{2} + \frac{1}{2} \cdot (2 (- x)) + \frac{1}{2} \cdot - 2$

Step 12.3.3

Rewrite the expression.

$6 x^{2} - x + \frac{1}{2} \cdot - 2$

Step 12.4

Cancel the common factor of

$2$ .

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Step 12.4.1

Factor

$2$ out of

$- 2$ .

$6 x^{2} - x + \frac{1}{2} \cdot (2 (- 1))$

Step 12.4.2

Cancel the common factor.

$6 x^{2} - x + \frac{1}{2} \cdot (2 \cdot - 1)$

Step 12.4.3

Rewrite the expression.

$6 x^{2} - x - 1$