Question

divide by using synthetic division. simplify your answer as much as possible.
$(b^{3}-216)\div(b-6)=\square$

Explanation:

Step1: Identify coefficients and root

Rewrite dividend as $b^3 + 0b^2 + 0b - 216$. Root of divisor $b-6$ is $6$. Coefficients: $1, 0, 0, -216$.

Step2: Set up synthetic division

Write root and coefficients:

$$\begin{array}{r|rrrr} 6 & 1 & 0 & 0 & -216 \\ \hline & & 6 & 36 & 216 \\ \hline & 1 & 6 & 36 & 0 \end{array}$$

Step3: Interpret the result

The last number is remainder ($0$). First three numbers are coefficients of quotient: $1, 6, 36$, so quotient is $b^2 + 6b + 36$.

Answer:

$b^2 + 6b + 36$