Divide Using Synthetic Division (2x^2-14x-7x^3+x^4)÷(7+x)

$(2 x^{2} - 14 x - 7 x^{3} + x^{4}) \div (7 + x)$

Step 1

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

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0				\xa0

Step 2

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

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0				\xa0
	$1$

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(- 7)$ and place the result of $(- 7)$ under the next term in the dividend $(- 7)$ .

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$			\xa0
	$1$

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.

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$			\xa0
	$1$	$- 14$

Step 5

Multiply the newest entry in the result $(- 14)$ by the divisor $(- 7)$ and place the result of $(98)$ under the next term in the dividend $(2)$ .

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$	$98$		\xa0
	$1$	$- 14$

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.

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$	$98$		\xa0
	$1$	$- 14$	$100$

Step 7

Multiply the newest entry in the result $(100)$ by the divisor $(- 7)$ and place the result of $(- 700)$ under the next term in the dividend $(- 14)$ .

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$	$98$	$- 700$	\xa0
	$1$	$- 14$	$100$

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.

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$	$98$	$- 700$	\xa0
	$1$	$- 14$	$100$	$- 714$

Step 9

Multiply the newest entry in the result $(- 714)$ by the divisor $(- 7)$ and place the result of $(4998)$ under the next term in the dividend $(0)$ .

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$	$98$	$- 700$	$4998$
	$1$	$- 14$	$100$	$- 714$

Step 10

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

$- 7$	$1$	$- 7$	$2$	$- 14$	$0$
	\xa0	$- 7$	$98$	$- 700$	$4998$
	$1$	$- 14$	$100$	$- 714$	$4998$

Step 11

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

$1 x^{3} + - 14 x^{2} + (100) x - 714 + \frac{4998}{x + 7}$

Step 12

Simplify the quotient polynomial.

$x^{3} - 14 x^{2} + 100 x - 714 + \frac{4998}{x + 7}$

Divide Using Synthetic Division (2x^2-14x-7x^3+x^4)÷(7+x)

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