Finite Math Examples

$\frac{4 m^{3} + 10 m^{2} + 4 m}{2 m^{2}}$

Step 1

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

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

Step 2

Divide the highest order term in the dividend $4 m^{3}$ by the highest order term in divisor $2 m^{2}$ .

$2 m$

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

Step 3

Multiply the new quotient term by the divisor.

$2 m$

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

$4 m^{3}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $4 m^{3} + 0 + 0$

$2 m$

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

$4 m^{3}$

$0$

Step 5

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

$2 m$

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

$4 m^{3}$

$0$

$10 m^{2}$

$4 m$

Step 6

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

$2 m$

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

$4 m^{3}$

$0$

$10 m^{2}$

$4 m$

$0$

Step 7

Divide the highest order term in the dividend $10 m^{2}$ by the highest order term in divisor $2 m^{2}$ .

$2 m$

$5$

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

$4 m^{3}$

$0$

$10 m^{2}$

$4 m$

$0$

Step 8

Multiply the new quotient term by the divisor.

$2 m$

$5$

$2 m^{2}$

$0 m$

$0$

$4 m^{3}$

$10 m^{2}$

$4 m$

$0$

$4 m^{3}$

$0$

$10 m^{2}$

$4 m$

$0$

$10 m^{2}$

$0$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $10 m^{2} + 0 + 0$

						$2 m$	+	$5$
$2 m^{2}$	+	$0 m$	+	$0$		$4 m^{3}$	+	$10 m^{2}$	+	$4 m$	+	$0$
					-	$4 m^{3}$	-	$0$	-	$0$
							+	$10 m^{2}$	+	$4 m$	+	$0$
							-	$10 m^{2}$	-	$0$	-	$0$

Step 10

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

						$2 m$	+	$5$
$2 m^{2}$	+	$0 m$	+	$0$		$4 m^{3}$	+	$10 m^{2}$	+	$4 m$	+	$0$
					-	$4 m^{3}$	-	$0$	-	$0$
							+	$10 m^{2}$	+	$4 m$	+	$0$
							-	$10 m^{2}$	-	$0$	-	$0$
									+	$4 m$	+	$0$

Step 11

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

$2 m + 5 + \frac{4 m}{2 m^{2}}$