Answer :

To evaluate the function [tex]\( f(x) = 6x^4 - 26x^3 - 23x^2 + 17x - 4 \)[/tex] at [tex]\( x = 5 \)[/tex], follow these steps:

1. Substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\[
f(5) = 6(5)^4 - 26(5)^3 - 23(5)^2 + 17(5) - 4
\][/tex]

2. Calculate each term individually:
- First, calculate [tex]\( 5^4 \)[/tex]:
[tex]\[
5^4 = 625
\][/tex]
- Then, [tex]\( 5^3 \)[/tex]:
[tex]\[
5^3 = 125
\][/tex]
- Next, [tex]\( 5^2 \)[/tex]:
[tex]\[
5^2 = 25
\][/tex]

3. Multiply each power of 5 by the corresponding coefficient:
- [tex]\( 6 \times 5^4 \)[/tex]:
[tex]\[
6 \times 625 = 3750
\][/tex]
- [tex]\(-26 \times 5^3 \)[/tex]:
[tex]\[
-26 \times 125 = -3250
\][/tex]
- [tex]\(-23 \times 5^2 \)[/tex]:
[tex]\[
-23 \times 25 = -575
\][/tex]
- [tex]\( 17 \times 5 \)[/tex]:
[tex]\[
17 \times 5 = 85
\][/tex]
- The constant term is [tex]\(-4\)[/tex].

4. Combine all the calculated terms:
[tex]\[
f(5) = 3750 - 3250 - 575 + 85 - 4
\][/tex]

5. Perform the addition and subtraction:
- [tex]\( 3750 - 3250 = 500 \)[/tex]
- [tex]\( 500 - 575 = -75 \)[/tex]
- [tex]\(-75 + 85 = 10\)[/tex]
- [tex]\(10 - 4 = 6\)[/tex]

So, the value of [tex]\( f(5) \)[/tex] is [tex]\( 6 \)[/tex].

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