Algebra Examples

$(2 x^{3} + 18 x + 5 x^{2} + 45) \div (2 x + 5)$

Step 1

Move $18 x$ .

$\frac{2 x^{3} + 5 x^{2} + 18 x + 45}{2 x + 5}$

Step 2

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

$2 x$

$5$

$2 x^{3}$

$5 x^{2}$

$18 x$

$45$

Step 3

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

					$x^{2}$
	$2 x$	+	$5$		$2 x^{3}$	+	$5 x^{2}$	+	$18 x$	+	$45$

Step 4

Multiply the new quotient term by the divisor.

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{3} + 5 x^{2}$

Step 6

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

Step 7

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

Step 8

Divide the highest order term in the dividend $18 x$ by the highest order term in divisor $2 x$ .

Step 9

Multiply the new quotient term by the divisor.

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $18 x + 45$

Step 11

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

Step 12

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

$x^{2} + 0 x + 9$