Answer :
To find the value of
[tex]$$
f(x)=5x^4-3x^2+6x+2
$$[/tex]
at [tex]$x = -2$[/tex], follow these steps:
1. Substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2)=5(-2)^4 - 3(-2)^2 + 6(-2) + 2.
$$[/tex]
2. Evaluate each term one by one:
- For the first term, compute [tex]$(-2)^4$[/tex]. Since
[tex]$$
(-2)^4 = 16,
$$[/tex]
we have
[tex]$$
5(-2)^4=5 \times 16=80.
$$[/tex]
- For the second term, compute [tex]$(-2)^2$[/tex]. Since
[tex]$$
(-2)^2 = 4,
$$[/tex]
we have
[tex]$$
-3(-2)^2=-3 \times 4=-12.
$$[/tex]
- For the third term:
[tex]$$
6(-2)=-12.
$$[/tex]
- The constant remains:
[tex]$$
+2.
$$[/tex]
3. Now, combine all the evaluated terms:
[tex]$$
f(-2)=80 - 12 - 12 + 2.
$$[/tex]
4. Perform the final calculation:
[tex]\[
80 - 12 = 68, \quad 68 - 12 = 56, \quad 56 + 2 = 58.
\][/tex]
Thus, the value of [tex]$f(-2)$[/tex] is
[tex]$$
\boxed{58}.
$$[/tex]
[tex]$$
f(x)=5x^4-3x^2+6x+2
$$[/tex]
at [tex]$x = -2$[/tex], follow these steps:
1. Substitute [tex]$x = -2$[/tex] into the function:
[tex]$$
f(-2)=5(-2)^4 - 3(-2)^2 + 6(-2) + 2.
$$[/tex]
2. Evaluate each term one by one:
- For the first term, compute [tex]$(-2)^4$[/tex]. Since
[tex]$$
(-2)^4 = 16,
$$[/tex]
we have
[tex]$$
5(-2)^4=5 \times 16=80.
$$[/tex]
- For the second term, compute [tex]$(-2)^2$[/tex]. Since
[tex]$$
(-2)^2 = 4,
$$[/tex]
we have
[tex]$$
-3(-2)^2=-3 \times 4=-12.
$$[/tex]
- For the third term:
[tex]$$
6(-2)=-12.
$$[/tex]
- The constant remains:
[tex]$$
+2.
$$[/tex]
3. Now, combine all the evaluated terms:
[tex]$$
f(-2)=80 - 12 - 12 + 2.
$$[/tex]
4. Perform the final calculation:
[tex]\[
80 - 12 = 68, \quad 68 - 12 = 56, \quad 56 + 2 = 58.
\][/tex]
Thus, the value of [tex]$f(-2)$[/tex] is
[tex]$$
\boxed{58}.
$$[/tex]
