Divide Using Synthetic Division (x^3-8x^2+17x-10)/(x-5)

$\frac{x^{3} - 8 x^{2} + 17 x - 10}{x - 5}$

Step 1

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

$5$	$1$	$- 8$	$17$	$- 10$
	\xa0			\xa0

Step 2

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

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(5)$ and place the result of $(5)$ under the next term in the dividend $(- 8)$ .

Step 4

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

Step 5

Multiply the newest entry in the result $(- 3)$ by the divisor $(5)$ and place the result of $(- 15)$ under the next term in the dividend $(17)$ .

Step 6

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

Step 7

Multiply the newest entry in the result $(2)$ by the divisor $(5)$ and place the result of $(10)$ under the next term in the dividend $(- 10)$ .

Step 8

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

Step 9

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

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

Step 10

Simplify the quotient polynomial.

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