Find the Quotient (x^5+x^3-1)÷(x-3)

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 ${\displaystyle x^5}$ by the highest order term in divisor ${\displaystyle x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle x^5-3x^4}$

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

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

Divide the highest order term in the dividend ${\displaystyle 3x^4}$ by the highest order term in divisor ${\displaystyle x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 3x^4-9x^3}$

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

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

Divide the highest order term in the dividend ${\displaystyle 10x^3}$ by the highest order term in divisor ${\displaystyle x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 10x^3-30x^2}$

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

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

Divide the highest order term in the dividend ${\displaystyle 30x^2}$ by the highest order term in divisor ${\displaystyle x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 30x^2-90x}$

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

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

Divide the highest order term in the dividend ${\displaystyle 90x}$ by the highest order term in divisor ${\displaystyle x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 90x-270}$

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