Pre-Algebra Examples

$4 x - 2$ , $2 x - 3$

Step 1

Divide $\frac{4 x - 2}{2 x - 3}$ using synthetic division and check if the remainder is equal to $0$ . If the remainder is equal to $0$ , it means that $2 x - 3$ is a factor for $4 x - 2$ . If the remainder is not equal to $0$ , it means that $2 x - 3$ is not a factor for $4 x - 2$ .

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Step 1.1

Divide each term in the denominator by $2$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{2} \cdot \frac{4 x - 2}{\frac{2 x - 3}{2}}$

Step 1.2

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

$\frac{3}{2}$	$4$	$- 2$

Step 1.3

The first number in the dividend $(4)$ is put into the first position of the result area (below the horizontal line).

$\frac{3}{2}$	$4$	$- 2$

	$4$

Step 1.4

Multiply the newest entry in the result $(4)$ by the divisor $(\frac{3}{2})$ and place the result of $(6)$ under the next term in the dividend $(- 2)$ .

$\frac{3}{2}$	$4$	$- 2$
		$6$
	$4$

Step 1.5

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

$\frac{3}{2}$	$4$	$- 2$
		$6$
	$4$	$4$

Step 1.6

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

$(\frac{1}{2}) \cdot (4 + \frac{4}{\frac{2 x - 3}{2}})$

Step 1.7

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (4 + \frac{8}{2 x - 3})$

Step 1.8

Simplify.

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Step 1.8.1

Apply the distributive property.

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

Step 1.8.2

Cancel the common factor of $2$ .

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Step 1.8.2.1

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot (2 (2)) + \frac{1}{2} \cdot \frac{8}{2 x - 3}$

Step 1.8.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2) + \frac{1}{2} \cdot \frac{8}{2 x - 3}$

Step 1.8.2.3

Rewrite the expression.

$2 + \frac{1}{2} \cdot \frac{8}{2 x - 3}$

Step 1.8.3

Cancel the common factor of $2$ .

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Step 1.8.3.1

Factor $2$ out of $8$ .

$2 + \frac{1}{2} \cdot \frac{2 (4)}{2 x - 3}$

Step 1.8.3.2

Cancel the common factor.

$2 + \frac{1}{2} \cdot \frac{2 \cdot 4}{2 x - 3}$

Step 1.8.3.3

Rewrite the expression.

$2 + \frac{4}{2 x - 3}$

Step 2

The remainder from dividing $\frac{4 x - 2}{2 x - 3}$ is $4$ , which is not equal to $0$ . The remainder is not equal to $0$ means that $2 x - 3$ is not a factor for $4 x - 2$ .

$2 x - 3$ is not a factor for $4 x - 2$