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Given the functions:

[tex] f(x) = -5x [/tex]

[tex] g(x) = 8x^2 - 5x - 9 [/tex]

Find [tex] (f \cdot g)(x) [/tex].

A. [tex] -40x^2 + 25x + 45x [/tex]

B. [tex] -40x^3 + 25x^2 + 45x [/tex]

C. [tex] -40x^4 + 25x^3 + 45x^2 [/tex]

D. [tex] -40x^3 - 5x - 9 [/tex]

Answer :

To solve the problem and find [tex]\((f \cdot g)(x)\)[/tex], we need to multiply the two functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].

1. Identify the functions:
- [tex]\(f(x) = -5x\)[/tex]
- [tex]\(g(x) = 8x^2 - 5x - 9\)[/tex]

2. Multiply the functions:
- The product [tex]\((f \cdot g)(x)\)[/tex] is found by multiplying each term in [tex]\(f(x)\)[/tex] with each term in [tex]\(g(x)\)[/tex].

3. Perform the multiplication:

[tex]\[
(-5x)(8x^2) = -40x^3
\][/tex]

[tex]\[
(-5x)(-5x) = 25x^2
\][/tex]

[tex]\[
(-5x)(-9) = 45x
\][/tex]

4. Combine the results:
- Sum all the terms from the multiplication to get the complete expression:

[tex]\[-40x^3 + 25x^2 + 45x\][/tex]

Therefore, the expression for [tex]\((f \cdot g)(x)\)[/tex] is [tex]\(-40x^3 + 25x^2 + 45x\)[/tex].

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