Algebra Examples

$\frac{g^{3} - 2 g^{2} + 3 g - 1}{g^{2} - 2 g}$

Step 1

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

$g^{2}$

$2 g$

$0$

$g^{3}$

$2 g^{2}$

$3 g$

$1$

Step 2

Divide the highest order term in the dividend $g^{3}$ by the highest order term in divisor $g^{2}$ .

$g$

$g^{2}$

$2 g$

$0$

$g^{3}$

$2 g^{2}$

$3 g$

$1$

Step 3

Multiply the new quotient term by the divisor.

$g$

$g^{2}$

$2 g$

$0$

$g^{3}$

$2 g^{2}$

$3 g$

$1$

$g^{3}$

$2 g^{2}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $g^{3} - 2 g^{2} + 0$

						$g$
$g^{2}$	-	$2 g$	+	$0$		$g^{3}$	-	$2 g^{2}$	+	$3 g$	-	$1$
					-	$g^{3}$	+	$2 g^{2}$	-	$0$

Step 5

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

$g$

$g^{2}$

$2 g$

$0$

$g^{3}$

$2 g^{2}$

$3 g$

$1$

$g^{3}$

$2 g^{2}$

$0$

$3 g$

Step 6

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

						$g$
$g^{2}$	-	$2 g$	+	$0$		$g^{3}$	-	$2 g^{2}$	+	$3 g$	-	$1$
					-	$g^{3}$	+	$2 g^{2}$	-	$0$
									+	$3 g$	-	$1$

Step 7

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

$g + \frac{3 g - 1}{g^{2} - 2 g}$