Divide Using Synthetic Division (4x^5-3x^4-14x^3+11x^2+8x-28)/(x-2)

$\frac{4 x^{5} - 3 x^{4} - 14 x^{3} + 11 x^{2} + 8 x - 28}{x - 2}$

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

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0					\xa0

The first number in the dividend $(4)$ is put into the first position of the result area (below the horizontal line).

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0					\xa0
	$4$

Multiply the newest entry in the result $(4)$ by the divisor $(2)$ and place the result of $(8)$ under the next term in the dividend $(- 3)$ .

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$				\xa0
	$4$

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

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$				\xa0
	$4$	$5$

Multiply the newest entry in the result $(5)$ by the divisor $(2)$ and place the result of $(10)$ under the next term in the dividend $(- 14)$ .

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$			\xa0
	$4$	$5$

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

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$			\xa0
	$4$	$5$	$- 4$

Multiply the newest entry in the result $(- 4)$ by the divisor $(2)$ and place the result of $(- 8)$ under the next term in the dividend $(11)$ .

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$	$- 8$		\xa0
	$4$	$5$	$- 4$

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

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$	$- 8$		\xa0
	$4$	$5$	$- 4$	$3$

Multiply the newest entry in the result $(3)$ by the divisor $(2)$ and place the result of $(6)$ under the next term in the dividend $(8)$ .

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$	$- 8$	$6$	\xa0
	$4$	$5$	$- 4$	$3$

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

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$	$- 8$	$6$	\xa0
	$4$	$5$	$- 4$	$3$	$14$

Multiply the newest entry in the result $(14)$ by the divisor $(2)$ and place the result of $(28)$ under the next term in the dividend $(- 28)$ .

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$	$- 8$	$6$	$28$
	$4$	$5$	$- 4$	$3$	$14$

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

$2$	$4$	$- 3$	$- 14$	$11$	$8$	$- 28$
	\xa0	$8$	$10$	$- 8$	$6$	$28$
	$4$	$5$	$- 4$	$3$	$14$	$0$

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

$4 x^{4} + 5 x^{3} - 4 x^{2} + 3 x + 14$

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