Divide Using Synthetic Division (12x^3+2x^2-5x+1)÷(x-1/3)

$(12 x^{3} + 2 x^{2} - 5 x + 1) \div (x - \frac{1}{3})$

Step 1

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

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0			\xa0

Step 2

The first number in the dividend $(12)$ is put into the first position of the result area (below the horizontal line).

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0			\xa0
	$12$

Step 3

Multiply the newest entry in the result $(12)$ by the divisor $(\frac{1}{3})$ and place the result of $(4)$ under the next term in the dividend $(2)$ .

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0	$4$		\xa0
	$12$

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.

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0	$4$		\xa0
	$12$	$6$

Step 5

Multiply the newest entry in the result $(6)$ by the divisor $(\frac{1}{3})$ and place the result of $(2)$ under the next term in the dividend $(- 5)$ .

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0	$4$	$2$	\xa0
	$12$	$6$

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.

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0	$4$	$2$	\xa0
	$12$	$6$	$- 3$

Step 7

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

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0	$4$	$2$	$- 1$
	$12$	$6$	$- 3$

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.

$\frac{1}{3}$	$12$	$2$	$- 5$	$1$
	\xa0	$4$	$2$	$- 1$
	$12$	$6$	$- 3$	$0$

Step 9

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

$12 x^{2} + 6 x - 3$

Divide Using Synthetic Division (12x^3+2x^2-5x+1)÷(x-1/3)

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