Divide Using Synthetic Division (14x^3+x^2-30x+13)/(7x-10)

$\frac{14 x^{3} + x^{2} - 30 x + 13}{7 x - 10}$

Step 1

Divide each term in the denominator by $7$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{7} \cdot \frac{14 x^{3} + x^{2} - 30 x + 13}{\frac{7 x - 10}{7}}$

Step 2

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

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0			\xa0

Step 3

The first number in the dividend $(14)$ is put into the first position of the result area (below the horizontal line).

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0			\xa0
	$14$

Step 4

Multiply the newest entry in the result $(14)$ by the divisor $(\frac{10}{7})$ and place the result of $(20)$ under the next term in the dividend $(1)$ .

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0	$20$		\xa0
	$14$

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.

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0	$20$		\xa0
	$14$	$21$

Step 6

Multiply the newest entry in the result $(21)$ by the divisor $(\frac{10}{7})$ and place the result of $(30)$ under the next term in the dividend $(- 30)$ .

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0	$20$	$30$	\xa0
	$14$	$21$

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.

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0	$20$	$30$	\xa0
	$14$	$21$	$0$

Step 8

Multiply the newest entry in the result $(0)$ by the divisor $(\frac{10}{7})$ and place the result of $(0)$ under the next term in the dividend $(13)$ .

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0	$20$	$30$	$0$
	$14$	$21$	$0$

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.

$\frac{10}{7}$	$14$	$1$	$- 30$	$13$
	\xa0	$20$	$30$	$0$
	$14$	$21$	$0$	$13$

Step 10

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

$(\frac{1}{7}) \cdot (14 x^{2} + 21 x + 0 + \frac{13}{\frac{7 x - 10}{7}})$

Step 11

Simplify the quotient polynomial.

$(\frac{1}{7}) \cdot (14 x^{2} + 21 x + \frac{91}{7 x - 10})$

Step 12

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{7} \cdot (14 x^{2} + 21 x) + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Apply the distributive property.

$\frac{1}{7} \cdot (14 x^{2}) + \frac{1}{7} \cdot (21 x) + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Cancel the common factor of $7$ .

Factor $7$ out of $14 x^{2}$ .

$\frac{1}{7} \cdot (7 (2 x^{2})) + \frac{1}{7} \cdot (21 x) + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Cancel the common factor.

$\frac{1}{7} \cdot (7 (2 x^{2})) + \frac{1}{7} \cdot (21 x) + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Rewrite the expression.

$2 x^{2} + \frac{1}{7} \cdot (21 x) + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Cancel the common factor of $7$ .

Factor $7$ out of $21 x$ .

$2 x^{2} + \frac{1}{7} \cdot (7 (3 x)) + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Cancel the common factor.

$2 x^{2} + \frac{1}{7} \cdot (7 (3 x)) + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Rewrite the expression.

$2 x^{2} + 3 x + \frac{1}{7} \cdot \frac{91}{7 x - 10}$

Cancel the common factor of $7$ .

Factor $7$ out of $91$ .

$2 x^{2} + 3 x + \frac{1}{7} \cdot \frac{7 (13)}{7 x - 10}$

Cancel the common factor.

$2 x^{2} + 3 x + \frac{1}{7} \cdot \frac{7 \cdot 13}{7 x - 10}$

Rewrite the expression.

$2 x^{2} + 3 x + \frac{13}{7 x - 10}$

Divide Using Synthetic Division (14x^3+x^2-30x+13)/(7x-10)

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