Q. 312 - Intermediate Algebra

Question

Divide each polynomial by the binomial. 

$\left(z^3+1\right)÷\left(z+1\right)$

Step-by-Step Solution

Answer

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

Step 1. Given information

Polynomial: $z^3+1$

Binomial: $z+1$

Step 2. Calculation

Using long division - 

         $z^2-z+1$

$z+1\overline{ )z^3+1 }$

          $z^3+z^2$

          $\overline{ - z^2+1}$

              $-z^2-z$ 

                  $\overline{ z+1}$

                        $z+1$

                       $\overline{ 0}$