Algebra Examples

$\frac{5 y^{4} z^{5}}{y^{4} z^{3}}$

Step 1

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

$y^{4} z^{3}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$5 z^{5} y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

Step 2

Divide the highest order term in the dividend $5 z^{5} y^{4}$ by the highest order term in divisor $y^{4} z^{3}$ .

$5 z^{2}$

$y^{4} z^{3}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$5 z^{5} y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

Step 3

Multiply the new quotient term by the divisor.

$5 z^{2}$

$y^{4} z^{3}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$5 z^{5} y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$5 z^{5} y^{4}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $5 z^{5} y^{4} + 0 + 0 + 0 + 0$

$5 z^{2}$

$y^{4} z^{3}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$5 z^{5} y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$5 z^{5} y^{4}$

$0$

Step 5

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

										$5 z^{2}$
$y^{4} z^{3}$	+	$0 y^{3}$	+	$0 y^{2}$	+	$0 y$	+	$0$		$5 z^{5} y^{4}$	+	$0 y^{3}$	+	$0 y^{2}$	+	$0 y$	+	$0$
									-	$5 z^{5} y^{4}$	-	$0$	-	$0$	-	$0$	-	$0$
																		$0$

Step 6

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

$5 z^{2}$