Divide Using Long Polynomial Division (f^2+7f+10)/(f+2)

$\frac{f^{2} + 7 f + 10}{f + 2}$

Step 1

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

$f$

$2$

$f^{2}$

$7 f$

$10$

Step 2

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

					$f$
	$f$	+	$2$		$f^{2}$	+	$7 f$	+	$10$

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 $f^{2} + 2 f$

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 $5 f$ by the highest order term in divisor $f$ .

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 $5 f + 10$

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.

$f + 5$