Answer :
To find [tex]\((f \cdot g)(x)\)[/tex], we need to multiply the two functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] together.
Firstly, let’s understand the functions:
1. [tex]\(f(x) = -5x\)[/tex]
2. [tex]\(g(x) = 8x^2 - 5x - 9\)[/tex]
The expression [tex]\((f \cdot g)(x)\)[/tex] means [tex]\(f(x) \times g(x)\)[/tex]. So, let's compute:
[tex]\[
f(x) \cdot g(x) = (-5x) \cdot (8x^2 - 5x - 9)
\][/tex]
Next, distribute [tex]\(-5x\)[/tex] to each term in [tex]\(g(x)\)[/tex]:
1. [tex]\(-5x \times 8x^2 = -40x^3\)[/tex]
2. [tex]\(-5x \times (-5x) = 25x^2\)[/tex]
3. [tex]\(-5x \times (-9) = 45x\)[/tex]
Now, putting it all together, the expanded form of the product is:
[tex]\[
-40x^3 + 25x^2 + 45x
\][/tex]
So the final answer is:
[tex]\(-40x^3 + 25x^2 + 45x\)[/tex]
Therefore, the correct choice from the options given is:
[tex]\(-40x^3 + 25x^2 + 45x\)[/tex]
Firstly, let’s understand the functions:
1. [tex]\(f(x) = -5x\)[/tex]
2. [tex]\(g(x) = 8x^2 - 5x - 9\)[/tex]
The expression [tex]\((f \cdot g)(x)\)[/tex] means [tex]\(f(x) \times g(x)\)[/tex]. So, let's compute:
[tex]\[
f(x) \cdot g(x) = (-5x) \cdot (8x^2 - 5x - 9)
\][/tex]
Next, distribute [tex]\(-5x\)[/tex] to each term in [tex]\(g(x)\)[/tex]:
1. [tex]\(-5x \times 8x^2 = -40x^3\)[/tex]
2. [tex]\(-5x \times (-5x) = 25x^2\)[/tex]
3. [tex]\(-5x \times (-9) = 45x\)[/tex]
Now, putting it all together, the expanded form of the product is:
[tex]\[
-40x^3 + 25x^2 + 45x
\][/tex]
So the final answer is:
[tex]\(-40x^3 + 25x^2 + 45x\)[/tex]
Therefore, the correct choice from the options given is:
[tex]\(-40x^3 + 25x^2 + 45x\)[/tex]
