Divide Using Synthetic Division (4d^4+3d^2-6d+1)/(2d+1)

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

Step 1

Divide each term in the denominator by $2$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{2} \cdot \frac{4 d^{4} + 3 d^{2} - 6 d + 1}{\frac{2 d + 1}{2}}$

Step 2

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

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0				\xa0

Step 3

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

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0				\xa0
	$4$

Step 4

Multiply the newest entry in the result $(4)$ by the divisor $(- \frac{1}{2})$ and place the result of $(- 2)$ under the next term in the dividend $(0)$ .

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$			\xa0
	$4$

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.

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$			\xa0
	$4$	$- 2$

Step 6

Multiply the newest entry in the result $(- 2)$ by the divisor $(- \frac{1}{2})$ and place the result of $(1)$ under the next term in the dividend $(3)$ .

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$	$1$		\xa0
	$4$	$- 2$

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.

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$	$1$		\xa0
	$4$	$- 2$	$4$

Step 8

Multiply the newest entry in the result $(4)$ by the divisor $(- \frac{1}{2})$ and place the result of $(- 2)$ under the next term in the dividend $(- 6)$ .

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$	$1$	$- 2$	\xa0
	$4$	$- 2$	$4$

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.

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$	$1$	$- 2$	\xa0
	$4$	$- 2$	$4$	$- 8$

Step 10

Multiply the newest entry in the result $(- 8)$ by the divisor $(- \frac{1}{2})$ and place the result of $(4)$ under the next term in the dividend $(1)$ .

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$	$1$	$- 2$	$4$
	$4$	$- 2$	$4$	$- 8$

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.

$- \frac{1}{2}$	$4$	$0$	$3$	$- 6$	$1$
	\xa0	$- 2$	$1$	$- 2$	$4$
	$4$	$- 2$	$4$	$- 8$	$5$

Step 12

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

$(\frac{1}{2}) \cdot (4 d^{3} + - 2 d^{2} + (4) d - 8 + \frac{5}{\frac{2 d + 1}{2}})$

Step 13

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (4 d^{3} - 2 d^{2} + 4 d - 8 + \frac{10}{2 d + 1})$

Step 14

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{2} \cdot (4 d^{3} - 2 d^{2} + 4 d - 8) + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Apply the distributive property.

$\frac{1}{2} \cdot (4 d^{3} - 2 d^{2} + 4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Apply the distributive property.

$\frac{1}{2} \cdot (4 d^{3} - 2 d^{2}) + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Apply the distributive property.

$\frac{1}{2} \cdot (4 d^{3}) + \frac{1}{2} \cdot (- 2 d^{2}) + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor of $2$ .

Factor $2$ out of $4 d^{3}$ .

$\frac{1}{2} \cdot (2 (2 d^{3})) + \frac{1}{2} \cdot (- 2 d^{2}) + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor.

$\frac{1}{2} \cdot (2 (2 d^{3})) + \frac{1}{2} \cdot (- 2 d^{2}) + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Rewrite the expression.

$2 d^{3} + \frac{1}{2} \cdot (- 2 d^{2}) + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 d^{2}$ .

$2 d^{3} + \frac{1}{2} \cdot (2 (- d^{2})) + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor.

$2 d^{3} + \frac{1}{2} \cdot (2 (- d^{2})) + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Rewrite the expression.

$2 d^{3} - d^{2} + \frac{1}{2} \cdot (4 d) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor of $2$ .

Factor $2$ out of $4 d$ .

$2 d^{3} - d^{2} + \frac{1}{2} \cdot (2 (2 d)) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor.

$2 d^{3} - d^{2} + \frac{1}{2} \cdot (2 (2 d)) + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Rewrite the expression.

$2 d^{3} - d^{2} + 2 d + \frac{1}{2} \cdot - 8 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$2 d^{3} - d^{2} + 2 d + \frac{1}{2} \cdot (2 (- 4)) + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor.

$2 d^{3} - d^{2} + 2 d + \frac{1}{2} \cdot (2 \cdot - 4) + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Rewrite the expression.

$2 d^{3} - d^{2} + 2 d - 4 + \frac{1}{2} \cdot \frac{10}{2 d + 1}$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$2 d^{3} - d^{2} + 2 d - 4 + \frac{1}{2} \cdot \frac{2 (5)}{2 d + 1}$

Cancel the common factor.

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

Rewrite the expression.

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

Divide Using Synthetic Division (4d^4+3d^2-6d+1)/(2d+1)

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