Algebra Examples

Use synthetic division to find the result when

x^{3} + 5 x^{2} - 9 x + 3

$x^{3} + 5 x^{2} - 9 x + 3$ is divided by

x - 1

$x - 1$

Step 1

Write the problem as a mathematical expression.

Use synthetic division to find the result when

\frac{x^{3} + 5 x^{2} - 9 x + 3}{x - 1}

$\frac{x^{3} + 5 x^{2} - 9 x + 3}{x - 1}$

Step 2

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

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$

Step 3

The first number in the dividend

(1)

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

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$

	$1$ $1$

Step 4

Multiply the newest entry in the result

(1)

$(1)$ by the divisor

(1)

$(1)$ and place the result of

(1)

$(1)$ under the next term in the dividend

(5)

$(5)$ .

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$
		$1$ $1$
	$1$ $1$

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.

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$
		$1$ $1$
	$1$ $1$	$6$ $6$

Step 6

Multiply the newest entry in the result

(6)

$(6)$ by the divisor

(1)

$(1)$ and place the result of

(6)

$(6)$ under the next term in the dividend

(- 9)

$(- 9)$ .

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$
		$1$ $1$	$6$ $6$
	$1$ $1$	$6$ $6$

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.

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$
		$1$ $1$	$6$ $6$
	$1$ $1$	$6$ $6$	$- 3$ $- 3$

Step 8

Multiply the newest entry in the result

(- 3)

$(- 3)$ by the divisor

(1)

$(1)$ and place the result of

(- 3)

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

(3)

$(3)$ .

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$
		$1$ $1$	$6$ $6$	$- 3$ $- 3$
	$1$ $1$	$6$ $6$	$- 3$ $- 3$

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.

$1$ $1$	$1$ $1$	$5$ $5$	$- 9$ $- 9$	$3$ $3$
		$1$ $1$	$6$ $6$	$- 3$ $- 3$
	$1$ $1$	$6$ $6$	$- 3$ $- 3$	$0$ $0$

Step 10

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

1 x^{2} + 6 x - 3

$1 x^{2} + 6 x - 3$

Step 11

Simplify the quotient polynomial.

x^{2} + 6 x - 3

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