Find the Factors Using the Factor Theorem 2x+6 , (x+3)

$2 x + 6$ , $(x + 3)$

Step 1

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

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

$- 3$	$2$	$6$
	\xa0	\xa0

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$- 3$	$2$	$6$
	\xa0	\xa0
	$2$

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

$- 3$	$2$	$6$
	\xa0	$- 6$
	$2$

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

$- 3$	$2$	$6$
	\xa0	$- 6$
	$2$	$0$

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

$2$

Step 2

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

$x + 3$ is a factor for $2 x + 6$

Step 3

Find all the possible roots for $2$ .

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.

$p = \pm 1, \pm 2$

$q = \pm 0$

Divide $2$ by $0$ .

Division by Zero

Step 4

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

$2$

Step 5

The factored polynomial is $(x + 3) (2)$ .

$(x + 3) (2)$

Find the Factors Using the Factor Theorem 2x+6 , (x+3)

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