Divide Using Synthetic Division (x^4y^4-x^3y^3-2x^2y^2+xy-5)÷(-xy-2)

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

Divide each term in the denominator by $- 1$ to make the coefficient of linear factor variable $1$ .

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

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

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0				\xa0

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

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0				\xa0
	$1$

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

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$			\xa0
	$1$

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

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$			\xa0
	$1$	$- 3$

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 $(- 2)$ .

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$	$6$		\xa0
	$1$	$- 3$

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

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$	$6$		\xa0
	$1$	$- 3$	$4$

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 $(1)$ .

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$	$6$	$- 8$	\xa0
	$1$	$- 3$	$4$

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

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$	$6$	$- 8$	\xa0
	$1$	$- 3$	$4$	$- 7$

Multiply the newest entry in the result $(- 7)$ by the divisor $(- 2)$ and place the result of $(14)$ under the next term in the dividend $(- 5)$ .

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$	$6$	$- 8$	$14$
	$1$	$- 3$	$4$	$- 7$

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

$- 2$	$1$	$- 1$	$- 2$	$1$	$- 5$
	\xa0	$- 2$	$6$	$- 8$	$14$
	$1$	$- 3$	$4$	$- 7$	$9$

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

$(\frac{1}{- 1}) \cdot (1 x^{3} + - 3 x^{2} + (4) x - 7 + \frac{9}{x y + 2})$

Simplify the quotient polynomial.

$(\frac{1}{- 1}) \cdot (x^{3} - 3 x^{2} + 4 x - 7 + \frac{9}{x y + 2})$

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{- 1} \cdot (x^{3} - 3 x^{2} + 4 x - 7) + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Apply the distributive property.

$\frac{1}{- 1} \cdot (x^{3} - 3 x^{2} + 4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Apply the distributive property.

$\frac{1}{- 1} \cdot (x^{3} - 3 x^{2}) + \frac{1}{- 1} \cdot (4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Apply the distributive property.

$\frac{1}{- 1} \cdot x^{3} + \frac{1}{- 1} \cdot (- 3 x^{2}) + \frac{1}{- 1} \cdot (4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Divide $1$ by $- 1$ .

$- 1 x^{3} + \frac{1}{- 1} \cdot (- 3 x^{2}) + \frac{1}{- 1} \cdot (4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Rewrite $- 1 x^{3}$ as $- x^{3}$ .

$- x^{3} + \frac{1}{- 1} \cdot (- 3 x^{2}) + \frac{1}{- 1} \cdot (4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Divide $1$ by $- 1$ .

$- x^{3} - 1 (- 3 x^{2}) + \frac{1}{- 1} \cdot (4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Multiply $- 3$ by $- 1$ .

$- x^{3} + 3 x^{2} + \frac{1}{- 1} \cdot (4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Divide $1$ by $- 1$ .

$- x^{3} + 3 x^{2} - 1 (4 x) + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Multiply $4$ by $- 1$ .

$- x^{3} + 3 x^{2} - 4 x + \frac{1}{- 1} \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Divide $1$ by $- 1$ .

$- x^{3} + 3 x^{2} - 4 x - 1 \cdot - 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Multiply $- 1$ by $- 7$ .

$- x^{3} + 3 x^{2} - 4 x + 7 + \frac{1}{- 1} \cdot \frac{9}{x y + 2}$

Divide $1$ by $- 1$ .

$- x^{3} + 3 x^{2} - 4 x + 7 - 1 \cdot \frac{9}{x y + 2}$

Multiply $- 1$ by $\frac{9}{x y + 2}$ .

$- x^{3} + 3 x^{2} - 4 x + 7 - 1 \frac{9}{x y + 2}$

Rewrite $- 1 \frac{9}{x y + 2}$ as $- \frac{9}{x y + 2}$ .

$- x^{3} + 3 x^{2} - 4 x + 7 - \frac{9}{x y + 2}$

Divide Using Synthetic Division (x^4y^4-x^3y^3-2x^2y^2+xy-5)÷(-xy-2)

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