Algebra Examples

$(10 r^{2} - 79 r + 63) \div (r - 7)$

Step 1

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

$r$

$7$

$10 r^{2}$

$79 r$

$63$

Step 2

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

					$10 r$
	$r$	-	$7$		$10 r^{2}$	-	$79 r$	+	$63$

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 $10 r^{2} - 70 r$

Step 5

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

Step 6

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

Step 7

Divide the highest order term in the dividend $- 9 r$ by the highest order term in divisor $r$ .

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 $- 9 r + 63$

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.

$10 r - 9$