Algebra Examples

$x^{3} - 3 x^{2} - 2 x + 6$ , $x - 4$

Step 1

Divide $\frac{x^{3} - 3 x^{2} - 2 x + 6}{x - 4}$ 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 $x^{3} - 3 x^{2} - 2 x + 6$ . If the remainder is not equal to $0$ , it means that $x - 4$ is not a factor for $x^{3} - 3 x^{2} - 2 x + 6$ .

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Step 1.1

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

$4$	$1$	$- 3$	$- 2$	$6$

Step 1.2

The first number in the dividend $(1)$ is put into the first position of the result area (below the horizontal line).

$4$	$1$	$- 3$	$- 2$	$6$

	$1$

Step 1.3

Multiply the newest entry in the result $(1)$ by the divisor $(4)$ and place the result of $(4)$ under the next term in the dividend $(- 3)$ .

$4$	$1$	$- 3$	$- 2$	$6$
		$4$
	$1$

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.

$4$	$1$	$- 3$	$- 2$	$6$
		$4$
	$1$	$1$

Step 1.5

Multiply the newest entry in the result $(1)$ by the divisor $(4)$ and place the result of $(4)$ under the next term in the dividend $(- 2)$ .

$4$	$1$	$- 3$	$- 2$	$6$
		$4$	$4$
	$1$	$1$

Step 1.6

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

$4$	$1$	$- 3$	$- 2$	$6$
		$4$	$4$
	$1$	$1$	$2$

Step 1.7

Multiply the newest entry in the result $(2)$ by the divisor $(4)$ and place the result of $(8)$ under the next term in the dividend $(6)$ .

$4$	$1$	$- 3$	$- 2$	$6$
		$4$	$4$	$8$
	$1$	$1$	$2$

Step 1.8

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

$4$	$1$	$- 3$	$- 2$	$6$
		$4$	$4$	$8$
	$1$	$1$	$2$	$14$

Step 1.9

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

$1 x^{2} + 1 x + 2 + \frac{14}{x - 4}$

Step 1.10

Simplify the quotient polynomial.

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

Step 2

The remainder from dividing $\frac{x^{3} - 3 x^{2} - 2 x + 6}{x - 4}$ is $14$ , which is not equal to $0$ . The remainder is not equal to $0$ means that $x - 4$ is not a factor for $x^{3} - 3 x^{2} - 2 x + 6$ .

$x - 4$ is not a factor for $x^{3} - 3 x^{2} - 2 x + 6$

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