Algebra Examples

$y^{9} \div y^{3}$

Step 1

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

$y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0 y^{8}$

$0 y^{7}$

$0 y^{6}$

$0 y^{5}$

$0 y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

Step 2

Divide the highest order term in the dividend $y^{9}$ by the highest order term in divisor $y^{3}$ .

$y^{6}$

$y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0 y^{8}$

$0 y^{7}$

$0 y^{6}$

$0 y^{5}$

$0 y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

Step 3

Multiply the new quotient term by the divisor.

$y^{6}$

$y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0 y^{8}$

$0 y^{7}$

$0 y^{6}$

$0 y^{5}$

$0 y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $y^{9} + 0 + 0 + 0$

$y^{6}$

$y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0 y^{8}$

$0 y^{7}$

$0 y^{6}$

$0 y^{5}$

$0 y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0$

Step 5

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

$y^{6}$

$y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0 y^{8}$

$0 y^{7}$

$0 y^{6}$

$0 y^{5}$

$0 y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0$

Step 6

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

$y^{6}$

$y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0 y^{8}$

$0 y^{7}$

$0 y^{6}$

$0 y^{5}$

$0 y^{4}$

$0 y^{3}$

$0 y^{2}$

$0 y$

$0$

$y^{9}$

$0$

$0 y^{5}$

$0 y^{4}$

$0 y^{3}$

$0 y^{2}$

Step 7

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

$y^{6}$