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

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

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$p$

$1$

$4 p^{3}$

$3 p^{2}$

$2 p$

$0$

Step 2

Divide the highest order term in the dividend $4 p^{3}$ by the highest order term in divisor $p$ .

					$4 p^{2}$
	$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$

Step 3

Multiply the new quotient term by the divisor.

				$4 p^{2}$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			+	$4 p^{3}$	-	$4 p^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $4 p^{3} - 4 p^{2}$

				$4 p^{2}$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$

Step 5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$4 p^{2}$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$

Step 6

Pull the next terms from the original dividend down into the current dividend.

				$4 p^{2}$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$

Step 7

Divide the highest order term in the dividend $p^{2}$ by the highest order term in divisor $p$ .

				$4 p^{2}$	+	$p$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$

Step 8

Multiply the new quotient term by the divisor.

				$4 p^{2}$	+	$p$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					+	$p^{2}$	-	$p$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $p^{2} - p$

				$4 p^{2}$	+	$p$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					-	$p^{2}$	+	$p$

Step 10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$4 p^{2}$	+	$p$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					-	$p^{2}$	+	$p$
							+	$3 p$

Step 11

Pull the next terms from the original dividend down into the current dividend.

				$4 p^{2}$	+	$p$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					-	$p^{2}$	+	$p$
							+	$3 p$	+	$0$

Step 12

Divide the highest order term in the dividend $3 p$ by the highest order term in divisor $p$ .

				$4 p^{2}$	+	$p$	+	$3$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					-	$p^{2}$	+	$p$
							+	$3 p$	+	$0$

Step 13

Multiply the new quotient term by the divisor.

				$4 p^{2}$	+	$p$	+	$3$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					-	$p^{2}$	+	$p$
							+	$3 p$	+	$0$
							+	$3 p$	-	$3$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $3 p - 3$

				$4 p^{2}$	+	$p$	+	$3$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					-	$p^{2}$	+	$p$
							+	$3 p$	+	$0$
							-	$3 p$	+	$3$

Step 15

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$4 p^{2}$	+	$p$	+	$3$
$p$	-	$1$		$4 p^{3}$	-	$3 p^{2}$	+	$2 p$	+	$0$
			-	$4 p^{3}$	+	$4 p^{2}$
					+	$p^{2}$	+	$2 p$
					-	$p^{2}$	+	$p$
							+	$3 p$	+	$0$
							-	$3 p$	+	$3$
									+	$3$

Step 16

The final answer is the quotient plus the remainder over the divisor.

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

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

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