Divide Using Synthetic Division 6x^5-2x^3+4x^2-3x+1 by x-2

$6 x^{5} - 2 x^{3} + 4 x^{2} - 3 x + 1$ by $x - 2$

Step 1

Write the problem as a mathematical expression.

$\frac{6 x^{5} - 2 x^{3} + 4 x^{2} - 3 x + 1}{x - 2}$

Step 2

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

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

Step 3

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
	$6$

Step 4

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
	$6$

Step 5

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
	$6$	$12$

Step 6

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
	$6$	$12$

Step 7

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
	$6$	$12$	$22$

Step 8

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
	$6$	$12$	$22$

Step 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.

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

Step 10

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
	$6$	$12$	$22$	$48$

Step 11

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
	$6$	$12$	$22$	$48$	$93$

Step 12

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	$12$	$24$	$44$	$96$	$186$
	$6$	$12$	$22$	$48$	$93$

Step 13

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	$12$	$24$	$44$	$96$	$186$
	$6$	$12$	$22$	$48$	$93$	$187$

Step 14

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