Algebra Examples

$3 x - 12$ , $(x - 4)$

Step 1

Divide $\frac{3 x - 12}{x - 4}$ using synthetic division and check if the remainder is equal to $0$ . If the remainder is equal to $0$ , it means that $x - 4$ is a factor for $3 x - 12$ . If the remainder is not equal to $0$ , it means that $x - 4$ is not a factor for $3 x - 12$ .

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Step 1.1

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

$4$	$3$	$- 12$

Step 1.2

The first number in the dividend $(3)$ is put into the first position of the result area (below the horizontal line).

$4$	$3$	$- 12$

	$3$

Step 1.3

Multiply the newest entry in the result $(3)$ by the divisor $(4)$ and place the result of $(12)$ under the next term in the dividend $(- 12)$ .

$4$	$3$	$- 12$
		$12$
	$3$

Step 1.4

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

$4$	$3$	$- 12$
		$12$
	$3$	$0$

Step 1.5

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

$3$

Step 2

The remainder from dividing $\frac{3 x - 12}{x - 4}$ is $0$ , which means that $x - 4$ is a factor for $3 x - 12$ .

$x - 4$ is a factor for $3 x - 12$

Step 3

Find all the possible roots for $3$ .

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Step 3.1

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 3$

$q = \pm 0$

Step 3.2

Divide $3$ by $0$ .

Division by Zero

Step 4

The final factor is the only factor left over from the synthetic division.

$3$

Step 5

The factored polynomial is $(x - 4) (3)$ .

$(x - 4) (3)$