Answer :

We are given the polynomial

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

To find [tex]\( f(-2) \)[/tex], substitute [tex]\( x=-2 \)[/tex] into the polynomial:

[tex]$$
f(-2)=5(-2)^4-3(-2)^2+6(-2)+2.
$$[/tex]

Step 1: Calculate each term.

1. For the term [tex]\(5(-2)^4\)[/tex]:
- [tex]\( (-2)^4 = 16 \)[/tex]
- [tex]\( 5 \times 16 = 80 \)[/tex]

2. For the term [tex]\(-3(-2)^2\)[/tex]:
- [tex]\( (-2)^2 = 4 \)[/tex]
- [tex]\( -3 \times 4 = -12 \)[/tex]

3. For the term [tex]\(6(-2)\)[/tex]:
- [tex]\( 6 \times (-2) = -12 \)[/tex]

4. The constant term is [tex]\(2\)[/tex].

Step 2: Sum all the terms:

[tex]$$
80 + (-12) + (-12) + 2 = 80 - 12 - 12 + 2.
$$[/tex]

First, calculate [tex]\(80 - 12 = 68\)[/tex]. Then, [tex]\(68 - 12 = 56\)[/tex]. Finally, [tex]\(56 + 2 = 58\)[/tex].

Thus, the value is

[tex]$$
f(-2)=58.
$$[/tex]

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Rewritten by : Barada