Question

if ( h(x) = 4x^2 - 7x - 1 ), use synthetic division to find ( h(3) ).

Explanation:

Step1: Set up synthetic division

For \( h(x) = 4x^2 - 7x - 1 \) and finding \( h(3) \), we use the root \( x = 3 \). The coefficients of the polynomial are \( 4, -7, -1 \).
Set up the synthetic division as:
\[

$$\begin{array}{r|rrr} 3 & 4 & -7 & -1 \\ & & 12 & 15 \\ \hline & 4 & 5 & 14 \\ \end{array}$$

\]

Step2: Interpret the result

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

Answer:

\( 14 \)