To find the value of [tex]\( h(n) \)[/tex] when [tex]\( n = -6 \)[/tex], we need to substitute [tex]\( n = -6 \)[/tex] into the given function [tex]\( h(n) = -n^3 - 5n^2 + 2n \)[/tex] and simplify step by step.
1. Start with the given function:
[tex]\[
h(n) = -n^3 - 5n^2 + 2n
\][/tex]
2. Substitute [tex]\( n = -6 \)[/tex] into the function:
[tex]\[
h(-6) = -(-6)^3 - 5(-6)^2 + 2(-6)
\][/tex]
3. Calculate [tex]\( (-6)^3 \)[/tex]:
[tex]\[
(-6)^3 = -216
\][/tex]
Then, the expression becomes:
[tex]\[
h(-6) = -(-216) - 5(-6)^2 + 2(-6)
\][/tex]
4. Simplify [tex]\(-(-216)\)[/tex]:
[tex]\[
-(-216) = 216
\][/tex]
So, our expression updates to:
[tex]\[
h(-6) = 216 - 5(-6)^2 + 2(-6)
\][/tex]
5. Calculate [tex]\( (-6)^2 \)[/tex]:
[tex]\[
(-6)^2 = 36
\][/tex]
So, we have:
[tex]\[
h(-6) = 216 - 5(36) + 2(-6)
\][/tex]
6. Calculate [tex]\( 5 \times 36 \)[/tex]:
[tex]\[
5 \times 36 = 180
\][/tex]
Thus, the expression updates to:
[tex]\[
h(-6) = 216 - 180 + 2(-6)
\][/tex]
7. Calculate [tex]\( 2 \times (-6) \)[/tex]:
[tex]\[
2 \times (-6) = -12
\][/tex]
So, we get:
[tex]\[
h(-6) = 216 - 180 - 12
\][/tex]
8. Finally, perform the arithmetic operations:
[tex]\[
216 - 180 = 36
\][/tex]
[tex]\[
36 - 12 = 24
\][/tex]
Therefore, the value of [tex]\( h(-6) \)[/tex] is:
[tex]\[
h(-6) = 24
\][/tex]
