Algebra Examples

$\frac{45 y^{4} + 15 y^{2} - 60}{- 15 y^{2} - 20}$

Step 1

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

$15 y^{2}$

$0 y$

$20$

$45 y^{4}$

$0 y^{3}$

$15 y^{2}$

$0 y$

$60$

Step 2

Divide the highest order term in the dividend $45 y^{4}$ by the highest order term in divisor $- 15 y^{2}$ .

$3 y^{2}$

$15 y^{2}$

$0 y$

$20$

$45 y^{4}$

$0 y^{3}$

$15 y^{2}$

$0 y$

$60$

Step 3

Multiply the new quotient term by the divisor.

$3 y^{2}$

$15 y^{2}$

$0 y$

$20$

$45 y^{4}$

$0 y^{3}$

$15 y^{2}$

$0 y$

$60$

$45 y^{4}$

$0$

$60 y^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $45 y^{4} + 0 + 60 y^{2}$

						-	$3 y^{2}$
-	$15 y^{2}$	+	$0 y$	-	$20$		$45 y^{4}$	+	$0 y^{3}$	+	$15 y^{2}$	+	$0 y$	-	$60$
						-	$45 y^{4}$	-	$0$	-	$60 y^{2}$

Step 5

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

						-	$3 y^{2}$
-	$15 y^{2}$	+	$0 y$	-	$20$		$45 y^{4}$	+	$0 y^{3}$	+	$15 y^{2}$	+	$0 y$	-	$60$
						-	$45 y^{4}$	-	$0$	-	$60 y^{2}$
										-	$45 y^{2}$

Step 6

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

						-	$3 y^{2}$
-	$15 y^{2}$	+	$0 y$	-	$20$		$45 y^{4}$	+	$0 y^{3}$	+	$15 y^{2}$	+	$0 y$	-	$60$
						-	$45 y^{4}$	-	$0$	-	$60 y^{2}$
										-	$45 y^{2}$	+	$0 y$	-	$60$

Step 7

Divide the highest order term in the dividend $- 45 y^{2}$ by the highest order term in divisor $- 15 y^{2}$ .

						-	$3 y^{2}$	+	$0 y$	+	$3$
-	$15 y^{2}$	+	$0 y$	-	$20$		$45 y^{4}$	+	$0 y^{3}$	+	$15 y^{2}$	+	$0 y$	-	$60$
						-	$45 y^{4}$	-	$0$	-	$60 y^{2}$
										-	$45 y^{2}$	+	$0 y$	-	$60$

Step 8

Multiply the new quotient term by the divisor.

						-	$3 y^{2}$	+	$0 y$	+	$3$
-	$15 y^{2}$	+	$0 y$	-	$20$		$45 y^{4}$	+	$0 y^{3}$	+	$15 y^{2}$	+	$0 y$	-	$60$
						-	$45 y^{4}$	-	$0$	-	$60 y^{2}$
										-	$45 y^{2}$	+	$0 y$	-	$60$
										-	$45 y^{2}$	+	$0$	-	$60$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 45 y^{2} + 0 - 60$

						-	$3 y^{2}$	+	$0 y$	+	$3$
-	$15 y^{2}$	+	$0 y$	-	$20$		$45 y^{4}$	+	$0 y^{3}$	+	$15 y^{2}$	+	$0 y$	-	$60$
						-	$45 y^{4}$	-	$0$	-	$60 y^{2}$
										-	$45 y^{2}$	+	$0 y$	-	$60$
										+	$45 y^{2}$	-	$0$	+	$60$

Step 10

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

						-	$3 y^{2}$	+	$0 y$	+	$3$
-	$15 y^{2}$	+	$0 y$	-	$20$		$45 y^{4}$	+	$0 y^{3}$	+	$15 y^{2}$	+	$0 y$	-	$60$
						-	$45 y^{4}$	-	$0$	-	$60 y^{2}$
										-	$45 y^{2}$	+	$0 y$	-	$60$
										+	$45 y^{2}$	-	$0$	+	$60$
															$0$

Step 11

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

$- 3 y^{2} + 0 y + 3$