To find [tex]\( P(-1) \)[/tex] for the function [tex]\( f(x) = (3x^2 + 2x)^3 \)[/tex], we need to evaluate the function at [tex]\( x = -1 \)[/tex].
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-1) = (3(-1)^2 + 2(-1))^3
\][/tex]
2. Calculate the expression inside the parentheses:
- First, compute [tex]\( (-1)^2 \)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
- Then, multiply by 3:
[tex]\[
3 \cdot 1 = 3
\][/tex]
- Next, compute [tex]\( 2 \cdot (-1) \)[/tex]:
[tex]\[
2 \cdot (-1) = -2
\][/tex]
- Add these results together:
[tex]\[
3 + (-2) = 1
\][/tex]
So, the expression inside the parentheses is 1.
3. Raise this result to the power of 3:
[tex]\[
(1)^3 = 1
\][/tex]
Therefore, the value of [tex]\( P(-1) \)[/tex] is [tex]\( 1 \)[/tex].
