Finite Math Examples

$\frac{27 x^{3} + 6 i x^{2} + 18 x + 4 i}{9 x + 2 i}$

Step 1

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

$9 x$

$2 i$

$27 x^{3}$

$6 i x^{2}$

$18 x$

$4 i$

Step 2

Divide the highest order term in the dividend $27 x^{3}$ by the highest order term in divisor $9 x$ .

					$3 x^{2}$
	$9 x$	+	$2 i$		$27 x^{3}$	+	$6 i x^{2}$	+	$18 x$	+	$4 i$

Step 3

Multiply the new quotient term by the divisor.

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $27 x^{3} + 6 x^{2} i$

Step 5

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

Step 6

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

Step 7

Divide the highest order term in the dividend $18 x$ by the highest order term in divisor $9 x$ .

Step 8

Multiply the new quotient term by the divisor.

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $18 x + 4 i$

Step 10

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

Step 11

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

$3 x^{2} + 0 x + 2$