Determine if the Expression is a Factor Using Synthetic Division 16x^3-144x^2-81x+729 ; x-9

$16 x^{3} - 144 x^{2} - 81 x + 729$ ; $x - 9$

Step 1

Divide $\frac{16 x^{3} - 144 x^{2} - 81 x + 729}{x - 9}$ 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 $16 x^{3} - 144 x^{2} - 81 x + 729$ . If the remainder is not equal to $0$ , it means that $x - 9$ is not a factor for $16 x^{3} - 144 x^{2} - 81 x + 729$ .

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

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0			\xa0

The first number in the dividend $(16)$ is put into the first position of the result area (below the horizontal line).

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0			\xa0
	$16$

Multiply the newest entry in the result $(16)$ by the divisor $(9)$ and place the result of $(144)$ under the next term in the dividend $(- 144)$ .

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0	$144$		\xa0
	$16$

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

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0	$144$		\xa0
	$16$	$0$

Multiply the newest entry in the result $(0)$ by the divisor $(9)$ and place the result of $(0)$ under the next term in the dividend $(- 81)$ .

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0	$144$	$0$	\xa0
	$16$	$0$

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

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0	$144$	$0$	\xa0
	$16$	$0$	$- 81$

Multiply the newest entry in the result $(- 81)$ by the divisor $(9)$ and place the result of $(- 729)$ under the next term in the dividend $(729)$ .

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0	$144$	$0$	$- 729$
	$16$	$0$	$- 81$

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

$9$	$16$	$- 144$	$- 81$	$729$
	\xa0	$144$	$0$	$- 729$
	$16$	$0$	$- 81$	$0$

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

$16 x^{2} + 0 x - 81$

Simplify the quotient polynomial.

$16 x^{2} - 81$

Step 2

The remainder from dividing $\frac{16 x^{3} - 144 x^{2} - 81 x + 729}{x - 9}$ is $0$ , which means that $x - 9$ is a factor for $16 x^{3} - 144 x^{2} - 81 x + 729$ .

$x - 9$ is a factor for $16 x^{3} - 144 x^{2} - 81 x + 729$

Determine if the Expression is a Factor Using Synthetic Division 16x^3-144x^2-81x+729 ; x-9

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