Answer :
We are given the function
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2.
$$[/tex]
To find [tex]$f(-2)$[/tex], we substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2) = 5(-2)^4 - 3(-2)^2 + 6(-2) + 2.
$$[/tex]
Step 1: Compute [tex]$(-2)^4$[/tex]
Recall that any number raised to an even power is positive:
[tex]$$
(-2)^4 = 16.
$$[/tex]
Then, the first term becomes:
[tex]$$
5(-2)^4 = 5 \times 16 = 80.
$$[/tex]
Step 2: Compute [tex]$(-2)^2$[/tex]
[tex]$$
(-2)^2 = 4.
$$[/tex]
Thus, the second term is:
[tex]$$
-3(-2)^2 = -3 \times 4 = -12.
$$[/tex]
Step 3: Compute [tex]$6(-2)$[/tex]
[tex]$$
6(-2) = -12.
$$[/tex]
Step 4: Add the constant term
The constant term is [tex]$2$[/tex].
Step 5: Sum all terms
Now, combine all the computed results:
[tex]$$
f(-2) = 80 + (-12) + (-12) + 2.
$$[/tex]
First, add the positive and negative parts:
[tex]$$
80 - 12 = 68,
$$[/tex]
[tex]$$
68 - 12 = 56,
$$[/tex]
Finally, add the constant:
[tex]$$
56 + 2 = 58.
$$[/tex]
Thus, the value of [tex]$f(-2)$[/tex] is
[tex]$$
\boxed{58}.
$$[/tex]
[tex]$$
f(x) = 5x^4 - 3x^2 + 6x + 2.
$$[/tex]
To find [tex]$f(-2)$[/tex], we substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2) = 5(-2)^4 - 3(-2)^2 + 6(-2) + 2.
$$[/tex]
Step 1: Compute [tex]$(-2)^4$[/tex]
Recall that any number raised to an even power is positive:
[tex]$$
(-2)^4 = 16.
$$[/tex]
Then, the first term becomes:
[tex]$$
5(-2)^4 = 5 \times 16 = 80.
$$[/tex]
Step 2: Compute [tex]$(-2)^2$[/tex]
[tex]$$
(-2)^2 = 4.
$$[/tex]
Thus, the second term is:
[tex]$$
-3(-2)^2 = -3 \times 4 = -12.
$$[/tex]
Step 3: Compute [tex]$6(-2)$[/tex]
[tex]$$
6(-2) = -12.
$$[/tex]
Step 4: Add the constant term
The constant term is [tex]$2$[/tex].
Step 5: Sum all terms
Now, combine all the computed results:
[tex]$$
f(-2) = 80 + (-12) + (-12) + 2.
$$[/tex]
First, add the positive and negative parts:
[tex]$$
80 - 12 = 68,
$$[/tex]
[tex]$$
68 - 12 = 56,
$$[/tex]
Finally, add the constant:
[tex]$$
56 + 2 = 58.
$$[/tex]
Thus, the value of [tex]$f(-2)$[/tex] is
[tex]$$
\boxed{58}.
$$[/tex]
