Answer :
We start by writing the given functions:
[tex]$$
f(x)=3x^3-5x \quad \text{and} \quad g(x)=3x^4.
$$[/tex]
To find the product [tex]$f(x) \cdot g(x)$[/tex], we multiply each term in [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
1. Multiply the first term of [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
[tex]$$
3x^3 \cdot 3x^4 = 9x^{3+4} = 9x^7.
$$[/tex]
2. Multiply the second term of [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
[tex]$$
(-5x) \cdot 3x^4 = -15x^{1+4} = -15x^5.
$$[/tex]
Now, add these two results together:
[tex]$$
f(x) \cdot g(x) = 9x^7 - 15x^5.
$$[/tex]
Thus, the final answer is:
[tex]$$
f(x) \cdot g(x) = 9x^7 - 15x^5.
$$[/tex]
Comparing this with the provided options, the correct choice is:
[tex]$$\textbf{(B)}\ 9x^7 - 15x^5.$$[/tex]
[tex]$$
f(x)=3x^3-5x \quad \text{and} \quad g(x)=3x^4.
$$[/tex]
To find the product [tex]$f(x) \cdot g(x)$[/tex], we multiply each term in [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
1. Multiply the first term of [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
[tex]$$
3x^3 \cdot 3x^4 = 9x^{3+4} = 9x^7.
$$[/tex]
2. Multiply the second term of [tex]$f(x)$[/tex] by [tex]$g(x)$[/tex]:
[tex]$$
(-5x) \cdot 3x^4 = -15x^{1+4} = -15x^5.
$$[/tex]
Now, add these two results together:
[tex]$$
f(x) \cdot g(x) = 9x^7 - 15x^5.
$$[/tex]
Thus, the final answer is:
[tex]$$
f(x) \cdot g(x) = 9x^7 - 15x^5.
$$[/tex]
Comparing this with the provided options, the correct choice is:
[tex]$$\textbf{(B)}\ 9x^7 - 15x^5.$$[/tex]
