if $p(x) = 3x^3 + 7x^2 - 5x - 25$, use synthetic division to find $p(-3)$.

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Accepted Answer

# Explanation:
## Step1: Set up synthetic division
For $ p(x) = 3x^3 + 7x^2 - 5x - 25 $ and $ x=-3 $, the coefficients are $ 3, 7, -5, -25 $. Write them in a row and put $ -3 $ outside the division bracket.
$$
\begin{array}{r|rrrr}
-3 & 3 & 7 & -5 & -25 \
 & & & & \
\hline
 & & & & \
\end{array}
$$
## Step2: Bring down the leading coefficient
Bring down the $ 3 $ to the bottom row.
$$
\begin{array}{r|rrrr}
-3 & 3 & 7 & -5 & -25 \
 & & & & \
\hline
 & 3 & & & \
\end{array}
$$
## Step3: Multiply and add
Multiply the brought - down number ($ 3 $) by $ -3 $: $ 3\times(-3)=-9 $. Add this to the next coefficient ($ 7 $): $ 7 + (-9)=-2 $.
$$
\begin{array}{r|rrrr}
-3 & 3 & 7 & -5 & -25 \
 & & -9 & & \
\hline
 & 3 & -2 & & \
\end{array}
$$
## Step4: Multiply and add again
Multiply the new number ($ -2 $) by $ -3 $: $ -2\times(-3) = 6 $. Add this to the next coefficient ($ -5 $): $ -5+6 = 1 $.
$$
\begin{array}{r|rrrr}
-3 & 3 & 7 & -5 & -25 \
 & & -9 & 6 & \
\hline
 & 3 & -2 & 1 & \
\end{array}
$$
## Step5: Multiply and add the last time
Multiply the new number ($ 1 $) by $ -3 $: $ 1\times(-3)=-3 $. Add this to the last coefficient ($ -25 $): $ -25+(-3)=-28 $.
$$
\begin{array}{r|rrrr}
-3 & 3 & 7 & -5 & -25 \
 & & -9 & 6 & -3 \
\hline
 & 3 & -2 & 1 & -28 \
\end{array}
$$
The last number in the bottom row is the value of $ p(-3) $.

# Answer:
$ -28 $

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QUESTION IMAGE

Question

Explanation:

Step1: Set up synthetic division

Step2: Bring down the leading coefficient

Step3: Multiply and add

Step4: Multiply and add again

Step5: Multiply and add the last time

Answer: