Answer :

To find the value of the function [tex]\( f(x) = x^2 + 8x^3 + 19x^2 + 32x + 60 \)[/tex] at [tex]\( x = -5 \)[/tex], follow these steps:

1. Substitute [tex]\( x = -5 \)[/tex] into the function:

[tex]\[
f(-5) = (-5)^2 + 8(-5)^3 + 19(-5)^2 + 32(-5) + 60
\][/tex]

2. Calculate each term separately:

- First term: [tex]\((-5)^2 = 25\)[/tex]
- Second term: [tex]\(8(-5)^3 = 8 \times (-125) = -1000\)[/tex]
- Third term: [tex]\(19(-5)^2 = 19 \times 25 = 475\)[/tex]
- Fourth term: [tex]\(32(-5) = -160\)[/tex]
- Fifth term: [tex]\(60\)[/tex]

3. Add all the terms together:

[tex]\[
f(-5) = 25 + (-1000) + 475 + (-160) + 60
\][/tex]

Combine the values step-by-step:

- [tex]\(25 + (-1000) = -975\)[/tex]
- [tex]\(-975 + 475 = -500\)[/tex]
- [tex]\(-500 + (-160) = -660\)[/tex]
- [tex]\(-660 + 60 = -600\)[/tex]

4. Final result:

The value of the function [tex]\( f(x) \)[/tex] at [tex]\( x = -5 \)[/tex] is [tex]\(-600\)[/tex].

Therefore, the solution for [tex]\( f(-5) \)[/tex] is [tex]\(-600\)[/tex].

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Rewritten by : Barada