Algebra Examples

$(- x^{2} - 2 x + 35) \div (5 - x)$

Step 1

Reorder $5$ and $- x$ .

$\frac{- x^{2} - 2 x + 35}{- x + 5}$

Step 2

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

$x$

$5$

$x^{2}$

$2 x$

$35$

Step 3

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

					$x$
-	$x$	+	$5$	-	$x^{2}$	-	$2 x$	+	$35$

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 $- x^{2} + 5 x$

Step 6

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

Step 7

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

Step 8

Divide the highest order term in the dividend $- 7 x$ by the highest order term in divisor $- x$ .

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 $- 7 x + 35$

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.

$x + 7$