Algebra Examples

$(24 k^{3} + 2 k^{2} + 24 k) \div 6$

Step 1

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

$6$

$24 k^{3}$

$2 k^{2}$

$24 k$

$0$

Step 2

Divide the highest order term in the dividend $24 k^{3}$ by the highest order term in divisor $6$ .

			$4 k^{3}$
	$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$

Step 3

Multiply the new quotient term by the divisor.

		$4 k^{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	+	$24 k^{3}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $24 k^{3}$

		$4 k^{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$

Step 5

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

		$4 k^{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$

Step 6

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

		$4 k^{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$

Step 7

Divide the highest order term in the dividend $2 k^{2}$ by the highest order term in divisor $6$ .

		$4 k^{3}$	+	$\frac{k^{2}}{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$

Step 8

Multiply the new quotient term by the divisor.

		$4 k^{3}$	+	$\frac{k^{2}}{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			+	$2 k^{2}$

Step 9

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

		$4 k^{3}$	+	$\frac{k^{2}}{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$

Step 10

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

		$4 k^{3}$	+	$\frac{k^{2}}{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$
				$0$

Step 11

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

		$4 k^{3}$	+	$\frac{k^{2}}{3}$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$
				$0$	+	$24 k$

Step 12

Divide the highest order term in the dividend $24 k$ by the highest order term in divisor $6$ .

		$4 k^{3}$	+	$\frac{k^{2}}{3}$	+	$4 k$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$
				$0$	+	$24 k$

Step 13

Multiply the new quotient term by the divisor.

		$4 k^{3}$	+	$\frac{k^{2}}{3}$	+	$4 k$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$
				$0$	+	$24 k$
					+	$24 k$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $24 k$

		$4 k^{3}$	+	$\frac{k^{2}}{3}$	+	$4 k$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$
				$0$	+	$24 k$
					-	$24 k$

Step 15

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

		$4 k^{3}$	+	$\frac{k^{2}}{3}$	+	$4 k$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$
				$0$	+	$24 k$
					-	$24 k$
						$0$

Step 16

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

		$4 k^{3}$	+	$\frac{k^{2}}{3}$	+	$4 k$
$6$		$24 k^{3}$	+	$2 k^{2}$	+	$24 k$	+	$0$
	-	$24 k^{3}$
		$0$	+	$2 k^{2}$
			-	$2 k^{2}$
				$0$	+	$24 k$
					-	$24 k$
						$0$	+	$0$

Step 17

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

$4 k^{3} + \frac{k^{2}}{3} + 4 k$