Algebra Examples

$(- 2 x - 3 + 8 x^{2}) \div (1 + 4 x)$

Step 1

Expand $- 2 x - 3 + 8 x^{2}$ .

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Step 1.1

Move $- 3$ .

$\frac{- 2 x + 8 x^{2} - 3}{1 + 4 x}$

Step 1.2

Reorder $- 2 x$ and $8 x^{2}$ .

$\frac{8 x^{2} - 2 x - 3}{1 + 4 x}$

Step 2

Reorder $1$ and $4 x$ .

$\frac{8 x^{2} - 2 x - 3}{4 x + 1}$

Step 3

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

$4 x$

$1$

$8 x^{2}$

$2 x$

$3$

Step 4

Divide the highest order term in the dividend $8 x^{2}$ by the highest order term in divisor $4 x$ .

					$2 x$
	$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$

Step 5

Multiply the new quotient term by the divisor.

				$2 x$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			+	$8 x^{2}$	+	$2 x$

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{2} + 2 x$

				$2 x$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			-	$8 x^{2}$	-	$2 x$

Step 7

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

				$2 x$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			-	$8 x^{2}$	-	$2 x$
					-	$4 x$

Step 8

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

				$2 x$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			-	$8 x^{2}$	-	$2 x$
					-	$4 x$	-	$3$

Step 9

Divide the highest order term in the dividend $- 4 x$ by the highest order term in divisor $4 x$ .

				$2 x$	-	$1$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			-	$8 x^{2}$	-	$2 x$
					-	$4 x$	-	$3$

Step 10

Multiply the new quotient term by the divisor.

				$2 x$	-	$1$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			-	$8 x^{2}$	-	$2 x$
					-	$4 x$	-	$3$
					-	$4 x$	-	$1$

Step 11

The expression needs to be subtracted from the dividend, so change all the signs in $- 4 x - 1$

				$2 x$	-	$1$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			-	$8 x^{2}$	-	$2 x$
					-	$4 x$	-	$3$
					+	$4 x$	+	$1$

Step 12

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

				$2 x$	-	$1$
$4 x$	+	$1$		$8 x^{2}$	-	$2 x$	-	$3$
			-	$8 x^{2}$	-	$2 x$
					-	$4 x$	-	$3$
					+	$4 x$	+	$1$
							-	$2$

Step 13

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

$2 x - 1 - \frac{2}{4 x + 1}$