Determine if the Expression is a Factor Using Synthetic Division 36x^3+60x^2-143x-242 ; x-2

$36 x^{3} + 60 x^{2} - 143 x - 242$ ; $x - 2$

Step 1

Divide $\frac{36 x^{3} + 60 x^{2} - 143 x - 242}{x - 2}$ using synthetic division and check if the remainder is equal to $0$ . If the remainder is equal to $0$ , it means that $x - 2$ is a factor for $36 x^{3} + 60 x^{2} - 143 x - 242$ . If the remainder is not equal to $0$ , it means that $x - 2$ is not a factor for $36 x^{3} + 60 x^{2} - 143 x - 242$ .

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

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0			\xa0

The first number in the dividend $(36)$ is put into the first position of the result area (below the horizontal line).

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0			\xa0
	$36$

Multiply the newest entry in the result $(36)$ by the divisor $(2)$ and place the result of $(72)$ under the next term in the dividend $(60)$ .

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0	$72$		\xa0
	$36$

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

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0	$72$		\xa0
	$36$	$132$

Multiply the newest entry in the result $(132)$ by the divisor $(2)$ and place the result of $(264)$ under the next term in the dividend $(- 143)$ .

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0	$72$	$264$	\xa0
	$36$	$132$

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

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0	$72$	$264$	\xa0
	$36$	$132$	$121$

Multiply the newest entry in the result $(121)$ by the divisor $(2)$ and place the result of $(242)$ under the next term in the dividend $(- 242)$ .

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0	$72$	$264$	$242$
	$36$	$132$	$121$

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

$2$	$36$	$60$	$- 143$	$- 242$
	\xa0	$72$	$264$	$242$
	$36$	$132$	$121$	$0$

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

$36 x^{2} + 132 x + 121$

Step 2

The remainder from dividing $\frac{36 x^{3} + 60 x^{2} - 143 x - 242}{x - 2}$ is $0$ , which means that $x - 2$ is a factor for $36 x^{3} + 60 x^{2} - 143 x - 242$ .

$x - 2$ is a factor for $36 x^{3} + 60 x^{2} - 143 x - 242$

Determine if the Expression is a Factor Using Synthetic Division 36x^3+60x^2-143x-242 ; x-2

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