Question

Divide each polynomial by the binomial.

$\left(z^3+1\right)÷\left(z+1\right)$

Short answer

The solution is$\left(z^2-z+1\right)$.

Step-by-step solution

Step 1. Given information 

Polynomial:$z^3+1$

Binomial:$z+1$

Step 2. Calculation 

Using long division -

$z^2-z+1$

role="math" localid="1645988083382" $z+1\overline{)z^3+1}$

$z^3+z^2$

role="math" localid="1645988173888" $\overline{-z^2+1}$

$-z^2-z$

$\overline{z+1}$

$z+1$

$\overline{0}$