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------------------------------------------------ Evaluate or simplify the expression for [tex]g(x) = 8x^5 - 58x^4 + 60x^3 + 140[/tex] when [tex]x = 6[/tex].

To solve the problem, we need to evaluate the polynomial function [tex]$ g(x) = 8x^5 - 58x^4 + 60x^3 + 140 $[/tex] at [tex]$ x = 6 $[/tex].

Here are the steps to find [tex]$ g(6) $[/tex]:

1. Substitute [tex]$ x $[/tex] with 6 in the polynomial:

[tex]\[
g(6) = 8(6)^5 - 58(6)^4 + 60(6)^3 + 140
\][/tex]

2. Calculate each term:

- [tex]$ 6^5 = 7776 $[/tex]
- Multiply by 8: [tex]$ 8 \times 7776 = 62208 $[/tex]

- [tex]$ 6^4 = 1296 $[/tex]
- Multiply by 58: [tex]$ 58 \times 1296 = 75168 $[/tex]

- [tex]$ 6^3 = 216 $[/tex]
- Multiply by 60: [tex]$ 60 \times 216 = 12960 $[/tex]

3. Combine these results:

Now put these values into the expression:
[tex]\[
g(6) = 62208 - 75168 + 12960 + 140
\][/tex]

4. Perform the addition and subtraction:

- Start with [tex]$ 62208 - 75168 = -12960 $[/tex]
- Then add [tex]$ 12960 $[/tex]: [tex]$-12960 + 12960 = 0$[/tex]
- Finally, add 140: [tex]$ 0 + 140 = 140 $[/tex]

Hence, the value of [tex]$ g(6) $[/tex] is [tex]$ 140 $[/tex].