Algebra Examples

$(- 3 x + 4 + 18 x^{2}) \div (5 + 6 x)$

Step 1

Expand $- 3 x + 4 + 18 x^{2}$ .

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Step 1.1

Move $4$ .

$\frac{- 3 x + 18 x^{2} + 4}{5 + 6 x}$

Step 1.2

Reorder $- 3 x$ and $18 x^{2}$ .

$\frac{18 x^{2} - 3 x + 4}{5 + 6 x}$

Step 2

Reorder $5$ and $6 x$ .

$\frac{18 x^{2} - 3 x + 4}{6 x + 5}$

Step 3

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

$6 x$

$5$

$18 x^{2}$

$3 x$

$4$

Step 4

Divide the highest order term in the dividend $18 x^{2}$ by the highest order term in divisor $6 x$ .

					$3 x$
	$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$

Step 5

Multiply the new quotient term by the divisor.

				$3 x$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			+	$18 x^{2}$	+	$15 x$

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $18 x^{2} + 15 x$

				$3 x$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			-	$18 x^{2}$	-	$15 x$

Step 7

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

				$3 x$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			-	$18 x^{2}$	-	$15 x$
					-	$18 x$

Step 8

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

				$3 x$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			-	$18 x^{2}$	-	$15 x$
					-	$18 x$	+	$4$

Step 9

Divide the highest order term in the dividend $- 18 x$ by the highest order term in divisor $6 x$ .

				$3 x$	-	$3$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			-	$18 x^{2}$	-	$15 x$
					-	$18 x$	+	$4$

Step 10

Multiply the new quotient term by the divisor.

				$3 x$	-	$3$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			-	$18 x^{2}$	-	$15 x$
					-	$18 x$	+	$4$
					-	$18 x$	-	$15$

Step 11

The expression needs to be subtracted from the dividend, so change all the signs in $- 18 x - 15$

				$3 x$	-	$3$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			-	$18 x^{2}$	-	$15 x$
					-	$18 x$	+	$4$
					+	$18 x$	+	$15$

Step 12

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

				$3 x$	-	$3$
$6 x$	+	$5$		$18 x^{2}$	-	$3 x$	+	$4$
			-	$18 x^{2}$	-	$15 x$
					-	$18 x$	+	$4$
					+	$18 x$	+	$15$
							+	$19$

Step 13

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

$3 x - 3 + \frac{19}{6 x + 5}$