Question

Use long division to divide. Specify the quotient and the remainder.(x3 − 734) ÷ (x − 9)quotient remainder

Answer 1

Let's begin dividing the leading term of the dividend by the leading term of the divisor

`(x^3)/(x)=x^2`

Multiply it by the divisor

`x^2\left(x−9\right)=x^3−9x^2`

Subtract the dividend from the obtained result

`\left(x^3−734\right)−\left(x^3−9x^2\right)=9x^2−734`

Divide the leading term of the obtained remainder by the leading term of the divisor

`(9x^2)/(x)=9x`

Multiply it by the divisor

`9x\left(x−9\right)=9x^2−81x`

Subtract the remainder from the obtained result

`\left(9x^2−734\right)−\left(9x^2−81x\right)=81x−734.`

Divide the leading term of the obtained remainder by the leading term of the divisor

`(81x)/(x)=81`

Multiply it by the divisor

`81\left(x−9\right)=81x−729`

Subtract the remainder from the obtained result

`\left(81x−734\right)−\left(81x−729\right)=−5`

since the degree of the remainder is less than the degree of the divisor, then we are done

`x^2+9x+81+−(5)/(x−9)`

The quotient is

`\begin{equation*} x^2+9x+81 \end{equation*}`

The remainder is

`-5`