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------------------------------------------------ Given: [tex]f(x) = 5x^4 - 3x^2 + 6x + 2[/tex]. Find [tex]f(-2)[/tex].

A. -28
B. 10
C. 14
D. 58
E. 82

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]