Question

if $g(t) = 2t^3 - 4t^2 - 17$, use synthetic division to find $g(3)$.

Explanation:

Step1: Set up synthetic division

We are dividing \(2t^{3}-4t^{2}+0t - 17\) (we add the \(0t\) term for the missing linear term) by \(t - 3\). The coefficients are \(2\), \(-4\), \(0\), \(-17\) and the root is \(t = 3\).
\[

$$\begin{array}{r|rrrr} 3 & 2 & -4 & 0 & -17 \\ & & 6 & 6 & 18 \\ \hline & 2 & 2 & 6 & 1 \\ \end{array}$$

\]

Step2: Interpret the result

The last number in the bottom row is the remainder, which is equal to \(g(3)\) by the Remainder Theorem.

Answer:

\(1\)