Divide Using Synthetic Division (4p^3-3p^2+2p)÷(p-1)

$(4 p^{3} - 3 p^{2} + 2 p) \div (p - 1)$

Step 1

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

$1$	$4$	$- 3$	$2$	$0$
	\xa0			\xa0

Step 2

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

Step 3

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 $(- 3)$ .

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 $(1)$ by the divisor $(1)$ and place the result of $(1)$ under the next term in the dividend $(2)$ .

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 $(3)$ by the divisor $(1)$ and place the result of $(3)$ under the next term in the dividend $(0)$ .

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.

$4 p^{2} + 1 p + 3 + \frac{3}{p - 1}$

Step 10

Simplify the quotient polynomial.

$4 p^{2} + p + 3 + \frac{3}{p - 1}$