Algebra Examples

Use synthetic division to find the result when

$4 x^{4} + 11 x^{3} - 9 x^{2} - 8 x + 30$ is divided by

$x + 3$

Step 1

Write the problem as a mathematical expression.

Use synthetic division to find the result when

$\frac{4 x^{4} + 11 x^{3} - 9 x^{2} - 8 x + 30}{x + 3}$

Step 2

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

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$

Step 3

The first number in the dividend

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

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$

	$4$

Step 4

Multiply the newest entry in the result

$(4)$ by the divisor

$(- 3)$ and place the result of

$(- 12)$ under the next term in the dividend

$(11)$ .

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$
	$4$

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.

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$
	$4$	$- 1$

Step 6

Multiply the newest entry in the result

$(- 1)$ by the divisor

$(- 3)$ and place the result of

$(3)$ under the next term in the dividend

$(- 9)$ .

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$	$3$
	$4$	$- 1$

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.

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$	$3$
	$4$	$- 1$	$- 6$

Step 8

Multiply the newest entry in the result

$(- 6)$ by the divisor

$(- 3)$ and place the result of

$(18)$ under the next term in the dividend

$(- 8)$ .

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$	$3$	$18$
	$4$	$- 1$	$- 6$

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.

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$	$3$	$18$
	$4$	$- 1$	$- 6$	$10$

Step 10

Multiply the newest entry in the result

$(10)$ by the divisor

$(- 3)$ and place the result of

$(- 30)$ under the next term in the dividend

$(30)$ .

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$	$3$	$18$	$- 30$
	$4$	$- 1$	$- 6$	$10$

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.

$- 3$	$4$	$11$	$- 9$	$- 8$	$30$
		$- 12$	$3$	$18$	$- 30$
	$4$	$- 1$	$- 6$	$10$	$0$

Step 12

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

$4 x^{3} + - 1 x^{2} + (- 6) x + 10$

Step 13

Simplify the quotient polynomial.

$4 x^{3} - x^{2} - 6 x + 10$