Divide Using Synthetic Division (x^3-5x^2+4x+7)÷(x-1)

$(x^{3} - 5 x^{2} + 4 x + 7) \div (x - 1)$

Step 1

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

$1$	$1$	$- 5$	$4$	$7$
	\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 $(1)$ and place the result of $(1)$ under the next term in the dividend $(- 5)$ .

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 $(- 4)$ by the divisor $(1)$ and place the result of $(- 4)$ under the next term in the dividend $(4)$ .

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 $(0)$ by the divisor $(1)$ and place the result of $(0)$ under the next term in the dividend $(7)$ .

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.

$1 x^{2} + - 4 x + 0 + \frac{7}{x - 1}$

Step 10

Simplify the quotient polynomial.

$x^{2} - 4 x + \frac{7}{x - 1}$