Divide Using Long Polynomial Division (7n^4-68n^3+46n^2-7n-18)÷(n-9)

$(7 n^{4} - 68 n^{3} + 46 n^{2} - 7 n - 18) \div (n - 9)$

Step 1

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

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

Step 2

Divide the highest order term in the dividend $7 n^{4}$ by the highest order term in divisor $n$ .

					$7 n^{3}$
	$n$	-	$9$		$7 n^{4}$	-	$68 n^{3}$	+	$46 n^{2}$	-	$7 n$	-	$18$

Step 3

Multiply the new quotient term by the divisor.

				$7 n^{3}$
$n$	-	$9$		$7 n^{4}$	-	$68 n^{3}$	+	$46 n^{2}$	-	$7 n$	-	$18$
			+	$7 n^{4}$	-	$63 n^{3}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $7 n^{4} - 63 n^{3}$

				$7 n^{3}$
$n$	-	$9$		$7 n^{4}$	-	$68 n^{3}$	+	$46 n^{2}$	-	$7 n$	-	$18$
			-	$7 n^{4}$	+	$63 n^{3}$

Step 5

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

				$7 n^{3}$
$n$	-	$9$		$7 n^{4}$	-	$68 n^{3}$	+	$46 n^{2}$	-	$7 n$	-	$18$
			-	$7 n^{4}$	+	$63 n^{3}$
					-	$5 n^{3}$

Step 6

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

$7 n^{3}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

Step 7

Divide the highest order term in the dividend $- 5 n^{3}$ by the highest order term in divisor $n$ .

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

Step 8

Multiply the new quotient term by the divisor.

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 5 n^{3} + 45 n^{2}$

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

Step 10

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

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

Step 11

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

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

Step 12

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

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

Step 13

Multiply the new quotient term by the divisor.

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $n^{2} - 9 n$

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

Step 15

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

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

$2 n$

Step 16

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

$7 n^{3}$

$5 n^{2}$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

$2 n$

$18$

Step 17

Divide the highest order term in the dividend $2 n$ by the highest order term in divisor $n$ .

$7 n^{3}$

$5 n^{2}$

$n$

$2$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

$2 n$

$18$

Step 18

Multiply the new quotient term by the divisor.

$7 n^{3}$

$5 n^{2}$

$n$

$2$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

$2 n$

$18$

$2 n$

$18$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $2 n - 18$

$7 n^{3}$

$5 n^{2}$

$n$

$2$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

$2 n$

$18$

$2 n$

$18$

Step 20

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

$7 n^{3}$

$5 n^{2}$

$n$

$2$

$n$

$9$

$7 n^{4}$

$68 n^{3}$

$46 n^{2}$

$7 n$

$18$

$7 n^{4}$

$63 n^{3}$

$5 n^{3}$

$46 n^{2}$

$5 n^{3}$

$45 n^{2}$

$n^{2}$

$7 n$

$n^{2}$

$9 n$

$2 n$

$18$

$2 n$

$18$

$0$

Step 21

Since the remander is $0$ , the final answer is the quotient.

$7 n^{3} - 5 n^{2} + n + 2$

Divide Using Long Polynomial Division (7n^4-68n^3+46n^2-7n-18)÷(n-9)

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