Divide Using Synthetic Division (6x^5-2x^3+4x^2-3x+1)÷(x-2)

$(6 x^{5} - 2 x^{3} + 4 x^{2} - 3 x + 1) \div (x - 2)$

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

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0					\xa0

The first number in the dividend $(6)$ is put into the first position of the result area (below the horizontal line).

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0					\xa0
	$6$

Multiply the newest entry in the result $(6)$ by the divisor $(2)$ and place the result of $(12)$ under the next term in the dividend $(0)$ .

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$				\xa0
	$6$

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

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$				\xa0
	$6$	$12$

Multiply the newest entry in the result $(12)$ by the divisor $(2)$ and place the result of $(24)$ under the next term in the dividend $(- 2)$ .

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$			\xa0
	$6$	$12$

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

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$			\xa0
	$6$	$12$	$22$

Multiply the newest entry in the result $(22)$ by the divisor $(2)$ and place the result of $(44)$ under the next term in the dividend $(4)$ .

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$	$44$		\xa0
	$6$	$12$	$22$

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

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$	$44$		\xa0
	$6$	$12$	$22$	$48$

Multiply the newest entry in the result $(48)$ by the divisor $(2)$ and place the result of $(96)$ under the next term in the dividend $(- 3)$ .

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$	$44$	$96$	\xa0
	$6$	$12$	$22$	$48$

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

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$	$44$	$96$	\xa0
	$6$	$12$	$22$	$48$	$93$

Multiply the newest entry in the result $(93)$ by the divisor $(2)$ and place the result of $(186)$ under the next term in the dividend $(1)$ .

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$	$44$	$96$	$186$
	$6$	$12$	$22$	$48$	$93$

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

$2$	$6$	$0$	$- 2$	$4$	$- 3$	$1$
	\xa0	$12$	$24$	$44$	$96$	$186$
	$6$	$12$	$22$	$48$	$93$	$187$

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

$6 x^{4} + 12 x^{3} + 22 x^{2} + 48 x + 93 + \frac{187}{x - 2}$

Related Questions