Determine if the Expression is a Factor Using Synthetic Division 100x^3-600x^2-9x+54 ; x-6

$100 x^{3} - 600 x^{2} - 9 x + 54$ ; $x - 6$

Step 1

Divide $\frac{100 x^{3} - 600 x^{2} - 9 x + 54}{x - 6}$ using synthetic division and check if the remainder is equal to $0$ . If the remainder is equal to $0$ , it means that $x - 6$ is a factor for $100 x^{3} - 600 x^{2} - 9 x + 54$ . If the remainder is not equal to $0$ , it means that $x - 6$ is not a factor for $100 x^{3} - 600 x^{2} - 9 x + 54$ .

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

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0			\xa0

The first number in the dividend $(100)$ is put into the first position of the result area (below the horizontal line).

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0			\xa0
	$100$

Multiply the newest entry in the result $(100)$ by the divisor $(6)$ and place the result of $(600)$ under the next term in the dividend $(- 600)$ .

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0	$600$		\xa0
	$100$

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

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0	$600$		\xa0
	$100$	$0$

Multiply the newest entry in the result $(0)$ by the divisor $(6)$ and place the result of $(0)$ under the next term in the dividend $(- 9)$ .

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0	$600$	$0$	\xa0
	$100$	$0$

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

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0	$600$	$0$	\xa0
	$100$	$0$	$- 9$

Multiply the newest entry in the result $(- 9)$ by the divisor $(6)$ and place the result of $(- 54)$ under the next term in the dividend $(54)$ .

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0	$600$	$0$	$- 54$
	$100$	$0$	$- 9$

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

$6$	$100$	$- 600$	$- 9$	$54$
	\xa0	$600$	$0$	$- 54$
	$100$	$0$	$- 9$	$0$

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

$100 x^{2} + 0 x - 9$

Simplify the quotient polynomial.

$100 x^{2} - 9$

Step 2

The remainder from dividing $\frac{100 x^{3} - 600 x^{2} - 9 x + 54}{x - 6}$ is $0$ , which means that $x - 6$ is a factor for $100 x^{3} - 600 x^{2} - 9 x + 54$ .

$x - 6$ is a factor for $100 x^{3} - 600 x^{2} - 9 x + 54$

Determine if the Expression is a Factor Using Synthetic Division 100x^3-600x^2-9x+54 ; x-6

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