Divide Using Synthetic Division (1/3x^3-2/9x^2+2/27x-1/81)/(x-1/3)

$\frac{\frac{1}{3} x^{3} - \frac{2}{9} x^{2} + \frac{2}{27} x - \frac{1}{81}}{x - \frac{1}{3}}$

Step 1

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

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0			\xa0

Step 2

The first number in the dividend $(\frac{1}{3})$ is put into the first position of the result area (below the horizontal line).

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0			\xa0
	$\frac{1}{3}$

Step 3

Multiply the newest entry in the result $(\frac{1}{3})$ by the divisor $(\frac{1}{3})$ and place the result of $(\frac{1}{9})$ under the next term in the dividend $(- \frac{2}{9})$ .

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0	$\frac{1}{9}$		\xa0
	$\frac{1}{3}$

Step 4

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

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0	$\frac{1}{9}$		\xa0
	$\frac{1}{3}$	$- \frac{1}{9}$

Step 5

Multiply the newest entry in the result $(- \frac{1}{9})$ by the divisor $(\frac{1}{3})$ and place the result of $(- \frac{1}{27})$ under the next term in the dividend $(\frac{2}{27})$ .

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0	$\frac{1}{9}$	$- \frac{1}{27}$	\xa0
	$\frac{1}{3}$	$- \frac{1}{9}$

Step 6

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

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0	$\frac{1}{9}$	$- \frac{1}{27}$	\xa0
	$\frac{1}{3}$	$- \frac{1}{9}$	$\frac{1}{27}$

Step 7

Multiply the newest entry in the result $(\frac{1}{27})$ by the divisor $(\frac{1}{3})$ and place the result of $(\frac{1}{81})$ under the next term in the dividend $(- \frac{1}{81})$ .

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0	$\frac{1}{9}$	$- \frac{1}{27}$	$\frac{1}{81}$
	$\frac{1}{3}$	$- \frac{1}{9}$	$\frac{1}{27}$

Step 8

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

$\frac{1}{3}$	$\frac{1}{3}$	$- \frac{2}{9}$	$\frac{2}{27}$	$- \frac{1}{81}$
	\xa0	$\frac{1}{9}$	$- \frac{1}{27}$	$\frac{1}{81}$
	$\frac{1}{3}$	$- \frac{1}{9}$	$\frac{1}{27}$	$0$

Step 9

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

$\frac{1}{3} x^{2} + - \frac{1}{9} x + \frac{1}{27}$

Step 10

Simplify the quotient polynomial.

$\frac{x^{2}}{3} - \frac{x}{9} + \frac{1}{27}$

Divide Using Synthetic Division (1/3x^3-2/9x^2+2/27x-1/81)/(x-1/3)

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