Determine if the Expression is a Factor Using Synthetic Division x^2+6x+9 , (x+3)

$x^{2} + 6 x + 9$ , $(x + 3)$

Step 1

Divide $\frac{x^{2} + 6 x + 9}{x + 3}$ using synthetic division and check if the remainder is equal to $0$ . If the remainder is equal to $0$ , it means that $x + 3$ is a factor for $x^{2} + 6 x + 9$ . If the remainder is not equal to $0$ , it means that $x + 3$ is not a factor for $x^{2} + 6 x + 9$ .

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

$- 3$	$1$	$6$	$9$
	\xa0		\xa0

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

$- 3$	$1$	$6$	$9$
	\xa0		\xa0
	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(- 3)$ and place the result of $(- 3)$ under the next term in the dividend $(6)$ .

$- 3$	$1$	$6$	$9$
	\xa0	$- 3$	\xa0
	$1$

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

$- 3$	$1$	$6$	$9$
	\xa0	$- 3$	\xa0
	$1$	$3$

Multiply the newest entry in the result $(3)$ by the divisor $(- 3)$ and place the result of $(- 9)$ under the next term in the dividend $(9)$ .

$- 3$	$1$	$6$	$9$
	\xa0	$- 3$	$- 9$
	$1$	$3$

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

$- 3$	$1$	$6$	$9$
	\xa0	$- 3$	$- 9$
	$1$	$3$	$0$

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

$(1) x + 3$

Simplify the quotient polynomial.

$x + 3$

Step 2

The remainder from dividing $\frac{x^{2} + 6 x + 9}{x + 3}$ is $0$ , which means that $x + 3$ is a factor for $x^{2} + 6 x + 9$ .

$x + 3$ is a factor for $x^{2} + 6 x + 9$

Determine if the Expression is a Factor Using Synthetic Division x^2+6x+9 , (x+3)

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