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].
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].
