College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Given [tex]f(x)=5x^2[/tex] and [tex]g(x)=x^3+2x^2-5x[/tex], what is [tex]f(x) \cdot g(x)[/tex]?

A. [tex]x^3+7x^2-5[/tex]
B. [tex]5x^6+10x^4-25x^2[/tex]
C. [tex]5x^5+10x^4-25x^3[/tex]
D. [tex]-x^3+3x^2+5x[/tex]

Answer :

Sure, let's find the product of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] step-by-step.

We are given:
[tex]\[ f(x) = 5x^2 \][/tex]
[tex]\[ g(x) = x^3 + 2x^2 - 5x \][/tex]

To find [tex]\( f(x) \cdot g(x) \)[/tex], we multiply these two functions together:

[tex]\[ f(x) \cdot g(x) = (5x^2) \cdot (x^3 + 2x^2 - 5x) \][/tex]

Let's distribute [tex]\( 5x^2 \)[/tex] across each term inside the parentheses:

1. [tex]\( 5x^2 \cdot x^3 = 5x^{2+3} = 5x^5 \)[/tex]
2. [tex]\( 5x^2 \cdot 2x^2 = 5 \cdot 2 \cdot x^{2+2} = 10x^4 \)[/tex]
3. [tex]\( 5x^2 \cdot (-5x) = 5 \cdot (-5) \cdot x^{2+1} = -25x^3 \)[/tex]

Now, we combine these results:

[tex]\[ f(x) \cdot g(x) = 5x^5 + 10x^4 - 25x^3 \][/tex]

So, the product [tex]\( f(x) \cdot g(x) \)[/tex] is:

[tex]\[ \boxed{5x^5 + 10x^4 - 25x^3} \][/tex]

Now let's compare this with the options provided:

- [tex]\( x^3 + 7x^2 - 5 \)[/tex]
- [tex]\( 5x^6 + 10x^4 - 25x^2 \)[/tex]
- [tex]\( 5x^5 + 10x^4 - 25x^3 \)[/tex]
- [tex]\( -x^3 + 3x^2 + 5x \)[/tex]

The correct option is:

[tex]\[ \boxed{5x^5 + 10x^4 - 25x^3} \][/tex]