Algebra Examples

$\frac{- 65 s^{4} + 86 s^{2} - 24}{- 5 s^{2} + 2}$

Step 1

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

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

Step 2

Divide the highest order term in the dividend $- 65 s^{4}$ by the highest order term in divisor $- 5 s^{2}$ .

$13 s^{2}$

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

Step 3

Multiply the new quotient term by the divisor.

$13 s^{2}$

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

$65 s^{4}$

$0$

$26 s^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $- 65 s^{4} + 0 + 26 s^{2}$

$13 s^{2}$

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

$65 s^{4}$

$0$

$26 s^{2}$

Step 5

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

$13 s^{2}$

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

$65 s^{4}$

$0$

$26 s^{2}$

$60 s^{2}$

Step 6

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

$13 s^{2}$

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

$65 s^{4}$

$0$

$26 s^{2}$

$60 s^{2}$

$0 s$

$24$

Step 7

Divide the highest order term in the dividend $60 s^{2}$ by the highest order term in divisor $- 5 s^{2}$ .

$13 s^{2}$

$0 s$

$12$

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

$65 s^{4}$

$0$

$26 s^{2}$

$60 s^{2}$

$0 s$

$24$

Step 8

Multiply the new quotient term by the divisor.

$13 s^{2}$

$0 s$

$12$

$5 s^{2}$

$0 s$

$2$

$65 s^{4}$

$0 s^{3}$

$86 s^{2}$

$0 s$

$24$

$65 s^{4}$

$0$

$26 s^{2}$

$60 s^{2}$

$0 s$

$24$

$60 s^{2}$

$0$

$24$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $60 s^{2} + 0 - 24$

							$13 s^{2}$	+	$0 s$	-	$12$
-	$5 s^{2}$	+	$0 s$	+	$2$	-	$65 s^{4}$	+	$0 s^{3}$	+	$86 s^{2}$	+	$0 s$	-	$24$
						+	$65 s^{4}$	-	$0$	-	$26 s^{2}$
										+	$60 s^{2}$	+	$0 s$	-	$24$
										-	$60 s^{2}$	-	$0$	+	$24$

Step 10

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

							$13 s^{2}$	+	$0 s$	-	$12$
-	$5 s^{2}$	+	$0 s$	+	$2$	-	$65 s^{4}$	+	$0 s^{3}$	+	$86 s^{2}$	+	$0 s$	-	$24$
						+	$65 s^{4}$	-	$0$	-	$26 s^{2}$
										+	$60 s^{2}$	+	$0 s$	-	$24$
										-	$60 s^{2}$	-	$0$	+	$24$
															$0$

Step 11

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

$13 s^{2} + 0 s - 12$