Question

if $f(x) = 9x^3 + 6x^2 + 33$, use synthetic division to find $f(-1)$. submit

Explanation:

Step1: Set up synthetic division

For \( f(x) = 9x^3 + 6x^2 + 0x + 33 \) (we include the \( 0x \) term for the missing \( x \) term) and we are dividing by \( x - (-1)=x + 1 \), so we use \( -1 \) in synthetic division.
The coefficients are \( 9, 6, 0, 33 \).
Set up the synthetic division as:
\[

$$\begin{array}{r|rrrr} -1 & 9 & 6 & 0 & 33 \\ & & -9 & 3 & -3 \\ \hline & 9 & -3 & 3 & 30 \\ \end{array}$$

\]

Step2: Interpret the result

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

Answer:

\( 30 \)