Question

use synthetic division to find the result when $x^3 + 6x^2 - x - 30$ is divided by $x + 5$.

Explanation:

Step1: Identify root of divisor

The divisor is $x+5$, so root is $x=-5$.

Step2: List coefficients of dividend

Dividend: $x^3+6x^2-x-30$, coefficients: $1, 6, -1, -30$

Step3: Set up synthetic division

$$\begin{array}{r|rrrr} -5 & 1 & 6 & -1 & -30 \\ \hline & & -5 & -5 & 30 \\ \hline & 1 & 1 & -6 & 0 \end{array}$$

Step4: Write quotient polynomial

The final coefficients $1,1,-6$ correspond to $x^2 + x - 6$, remainder is $0$.

Answer:

$x^2 + x - 6$