Question

if $f(x) = 38x^2 - 30x + 14$, use synthetic division to find $f(1)$.

Explanation:

Step1: Set up synthetic division

For \( f(x) = 38x^2 - 30x + 14 \), we use \( x = 1 \) for synthetic division. The coefficients are \( 38 \), \( -30 \), \( 14 \).
\[

$$\begin{array}{r|rrr} 1 & 38 & -30 & 14 \\ & & 38 & 8 \\ \hline & 38 & 8 & 22 \\ \end{array}$$

\]

Step2: Interpret the result

The last number in the bottom row is the remainder, which is \( f(1) \).

Answer:

22