Find the Quotient (9-x^2)/(3x)

Reorder ${\displaystyle 9}$ and ${\displaystyle -x^2}$.

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

Divide the highest order term in the dividend ${\displaystyle -x^2}$ by the highest order term in divisor ${\displaystyle 3x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle -x^2+0}$

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

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