Answer :
We are given the function
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2
$$[/tex]
and we need to calculate [tex]$f(-2)$[/tex].
Step 1: Substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2) = 5(-2)^4 - 3(-2)^2 + 6(-2) + 2
$$[/tex]
Step 2: Evaluate each term one by one.
1. Calculate [tex]$(-2)^4$[/tex]:
[tex]$$
(-2)^4 = 16
$$[/tex]
Then the first term is:
[tex]$$
5(-2)^4 = 5 \times 16 = 80
$$[/tex]
2. Calculate [tex]$(-2)^2$[/tex]:
[tex]$$
(-2)^2 = 4
$$[/tex]
Then the second term is:
[tex]$$
-3(-2)^2 = -3 \times 4 = -12
$$[/tex]
3. Evaluate the third term:
[tex]$$
6(-2) = -12
$$[/tex]
4. The constant term remains:
[tex]$$
2
$$[/tex]
Step 3: Combine all terms:
[tex]$$
f(-2) = 80 - 12 - 12 + 2
$$[/tex]
Step 4: Perform the arithmetic step-by-step:
\begin{align}
80 - 12 &= 68, \\
68 - 12 &= 56, \\
56 + 2 &= 58.
\end{align}
Thus, the final result is:
[tex]$$
f(-2) = 58.
$$[/tex]
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2
$$[/tex]
and we need to calculate [tex]$f(-2)$[/tex].
Step 1: Substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2) = 5(-2)^4 - 3(-2)^2 + 6(-2) + 2
$$[/tex]
Step 2: Evaluate each term one by one.
1. Calculate [tex]$(-2)^4$[/tex]:
[tex]$$
(-2)^4 = 16
$$[/tex]
Then the first term is:
[tex]$$
5(-2)^4 = 5 \times 16 = 80
$$[/tex]
2. Calculate [tex]$(-2)^2$[/tex]:
[tex]$$
(-2)^2 = 4
$$[/tex]
Then the second term is:
[tex]$$
-3(-2)^2 = -3 \times 4 = -12
$$[/tex]
3. Evaluate the third term:
[tex]$$
6(-2) = -12
$$[/tex]
4. The constant term remains:
[tex]$$
2
$$[/tex]
Step 3: Combine all terms:
[tex]$$
f(-2) = 80 - 12 - 12 + 2
$$[/tex]
Step 4: Perform the arithmetic step-by-step:
\begin{align}
80 - 12 &= 68, \\
68 - 12 &= 56, \\
56 + 2 &= 58.
\end{align}
Thus, the final result is:
[tex]$$
f(-2) = 58.
$$[/tex]
