Question

if $p(z) = 7z^{2} + 9z + 17$, use synthetic division to find $p(1)$.

Explanation:

Step1: Set up synthetic division

For the polynomial \( p(z) = 7z^2 + 9z + 17 \) and \( z = 1 \), we set up synthetic division with the root \( 1 \) and the coefficients \( 7, 9, 17 \).
\[

$$\begin{array}{r|rrr} 1 & 7 & 9 & 17 \\ & & 7 & 16 \\ \hline & 7 & 16 & 33 \\ \end{array}$$

\]

Step2: Interpret the result

The last number in the bottom row of the synthetic division is the value of \( p(1) \).

Answer:

\( 33 \)