Algebra Examples

$x^{2} - 81$ , $x + 9$

Step 1

Divide $\frac{x^{2} - 81}{x + 9}$ using synthetic division and check if the remainder is equal to $0$ . If the remainder is equal to $0$ , it means that $x + 9$ is a factor for $x^{2} - 81$ . If the remainder is not equal to $0$ , it means that $x + 9$ is not a factor for $x^{2} - 81$ .

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Step 1.1

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

$- 9$	$1$	$0$	$- 81$

Step 1.2

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

$- 9$	$1$	$0$	$- 81$

	$1$

Step 1.3

Multiply the newest entry in the result $(1)$ by the divisor $(- 9)$ and place the result of $(- 9)$ under the next term in the dividend $(0)$ .

$- 9$	$1$	$0$	$- 81$
		$- 9$
	$1$

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.

$- 9$	$1$	$0$	$- 81$
		$- 9$
	$1$	$- 9$

Step 1.5

Multiply the newest entry in the result $(- 9)$ by the divisor $(- 9)$ and place the result of $(81)$ under the next term in the dividend $(- 81)$ .

$- 9$	$1$	$0$	$- 81$
		$- 9$	$81$
	$1$	$- 9$

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.

$- 9$	$1$	$0$	$- 81$
		$- 9$	$81$
	$1$	$- 9$	$0$

Step 1.7

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

$(1) x - 9$

Step 1.8

Simplify the quotient polynomial.

$x - 9$

Step 2

The remainder from dividing $\frac{x^{2} - 81}{x + 9}$ is $0$ , which means that $x + 9$ is a factor for $x^{2} - 81$ .

$x + 9$ is a factor for $x^{2} - 81$

Step 3

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

$x - 9$

Step 4

The factored polynomial is $(x + 9) (x - 9)$ .

$(x + 9) (x - 9)$