Divide Using Synthetic Division (5x^4-3x+1)/(4-x)

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

Step 1

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

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

Step 2

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

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0				\xa0

Step 3

The first number in the dividend $(5)$ is put into the first position of the result area (below the horizontal line).

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0				\xa0
	$5$

Step 4

Multiply the newest entry in the result $(5)$ by the divisor $(4)$ and place the result of $(20)$ under the next term in the dividend $(0)$ .

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$			\xa0
	$5$

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.

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$			\xa0
	$5$	$20$

Step 6

Multiply the newest entry in the result $(20)$ by the divisor $(4)$ and place the result of $(80)$ under the next term in the dividend $(0)$ .

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$	$80$		\xa0
	$5$	$20$

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.

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$	$80$		\xa0
	$5$	$20$	$80$

Step 8

Multiply the newest entry in the result $(80)$ by the divisor $(4)$ and place the result of $(320)$ under the next term in the dividend $(- 3)$ .

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$	$80$	$320$	\xa0
	$5$	$20$	$80$

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.

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$	$80$	$320$	\xa0
	$5$	$20$	$80$	$317$

Step 10

Multiply the newest entry in the result $(317)$ by the divisor $(4)$ and place the result of $(1268)$ under the next term in the dividend $(1)$ .

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$	$80$	$320$	$1268$
	$5$	$20$	$80$	$317$

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.

$4$	$5$	$0$	$0$	$- 3$	$1$
	\xa0	$20$	$80$	$320$	$1268$
	$5$	$20$	$80$	$317$	$1269$

Step 12

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

$(\frac{1}{- 1}) \cdot (5 x^{3} + 20 x^{2} + (80) x + 317 + \frac{1269}{x - 4})$

Step 13

Simplify the quotient polynomial.

$(\frac{1}{- 1}) \cdot (5 x^{3} + 20 x^{2} + 80 x + 317 + \frac{1269}{x - 4})$

Step 14

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{- 1} \cdot (5 x^{3} + 20 x^{2} + 80 x + 317) + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Apply the distributive property.

$\frac{1}{- 1} \cdot (5 x^{3} + 20 x^{2} + 80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Apply the distributive property.

$\frac{1}{- 1} \cdot (5 x^{3} + 20 x^{2}) + \frac{1}{- 1} \cdot (80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Apply the distributive property.

$\frac{1}{- 1} \cdot (5 x^{3}) + \frac{1}{- 1} \cdot (20 x^{2}) + \frac{1}{- 1} \cdot (80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Divide $1$ by $- 1$ .

$- 1 (5 x^{3}) + \frac{1}{- 1} \cdot (20 x^{2}) + \frac{1}{- 1} \cdot (80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Multiply $5$ by $- 1$ .

$- 5 x^{3} + \frac{1}{- 1} \cdot (20 x^{2}) + \frac{1}{- 1} \cdot (80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Divide $1$ by $- 1$ .

$- 5 x^{3} - 1 (20 x^{2}) + \frac{1}{- 1} \cdot (80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Multiply $20$ by $- 1$ .

$- 5 x^{3} - 20 x^{2} + \frac{1}{- 1} \cdot (80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Divide $1$ by $- 1$ .

$- 5 x^{3} - 20 x^{2} - 1 (80 x) + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Multiply $80$ by $- 1$ .

$- 5 x^{3} - 20 x^{2} - 80 x + \frac{1}{- 1} \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Divide $1$ by $- 1$ .

$- 5 x^{3} - 20 x^{2} - 80 x - 1 \cdot 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Multiply $- 1$ by $317$ .

$- 5 x^{3} - 20 x^{2} - 80 x - 317 + \frac{1}{- 1} \cdot \frac{1269}{x - 4}$

Divide $1$ by $- 1$ .

$- 5 x^{3} - 20 x^{2} - 80 x - 317 - 1 \cdot \frac{1269}{x - 4}$

Multiply $- 1$ by $\frac{1269}{x - 4}$ .

$- 5 x^{3} - 20 x^{2} - 80 x - 317 - 1 \frac{1269}{x - 4}$

Rewrite $- 1 \frac{1269}{x - 4}$ as $- \frac{1269}{x - 4}$ .

$- 5 x^{3} - 20 x^{2} - 80 x - 317 - \frac{1269}{x - 4}$

Divide Using Synthetic Division (5x^4-3x+1)/(4-x)

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