High School

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\[
\begin{array}{l}
f(x) = -5x \\
g(x) = 8x^2 - 5x - 9 \\
\text{Find } (f \cdot g)(x) \\
\text{A. } -40x^2 + 25x + 45x \\
\text{B. } -40x^3 + 25x^2 + 45x \\
\text{C. } -40x^4 + 25x^3 + 45x^2 \\
\text{D. } -40x^3 - 5x - 9 \\
\end{array}
\]

Answer :

To find [tex]\((f \cdot g)(x)\)[/tex], we'll multiply the two given functions, [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].

1. Functions Overview:

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

2. Multiply [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:

Multiply [tex]\(f(x) = -5x\)[/tex] by each term in [tex]\(g(x) = 8x^2 - 5x - 9\)[/tex]:

- [tex]\(-5x \cdot 8x^2 = -40x^3\)[/tex]
- [tex]\(-5x \cdot (-5x) = 25x^2\)[/tex]
- [tex]\(-5x \cdot (-9) = 45x\)[/tex]

3. Combine the results:

Combine all the terms from the multiplication step:

[tex]\[
(f \cdot g)(x) = -40x^3 + 25x^2 + 45x
\][/tex]

So, the result of [tex]\( (f \cdot g)(x) \)[/tex] is [tex]\(-40x^3 + 25x^2 + 45x\)[/tex].

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Rewritten by : Barada