Answer :
Sure, let's solve this step-by-step.
We have two functions:
[tex]\[ f(x) = 5x^2 \][/tex]
[tex]\[ g(x) = x^3 + 2x^2 - 5x \][/tex]
We need to find [tex]\( f(x) \cdot g(x) \)[/tex], which means we will multiply [tex]\( f(x) \)[/tex] by [tex]\( g(x) \)[/tex].
First, write down the multiplication:
[tex]\[ f(x) \cdot g(x) = (5x^2) \cdot (x^3 + 2x^2 - 5x) \][/tex]
Now distribute [tex]\( 5x^2 \)[/tex] to each term inside the parentheses:
[tex]\[ 5x^2 \cdot x^3 + 5x^2 \cdot 2x^2 + 5x^2 \cdot (-5x) \][/tex]
Now calculate each term separately:
1. [tex]\( 5x^2 \cdot x^3 = 5x^{2+3} = 5x^5 \)[/tex]
2. [tex]\( 5x^2 \cdot 2x^2 = 10x^{2+2} = 10x^4 \)[/tex]
3. [tex]\( 5x^2 \cdot (-5x) = -25x^{2+1} = -25x^3 \)[/tex]
So, combine these together:
[tex]\[ f(x) \cdot g(x) = 5x^5 + 10x^4 - 25x^3 \][/tex]
From the given choices, the correct answer is:
[tex]\[ \boxed{5x^5 + 10x^4 - 25x^3} \][/tex]
We have two functions:
[tex]\[ f(x) = 5x^2 \][/tex]
[tex]\[ g(x) = x^3 + 2x^2 - 5x \][/tex]
We need to find [tex]\( f(x) \cdot g(x) \)[/tex], which means we will multiply [tex]\( f(x) \)[/tex] by [tex]\( g(x) \)[/tex].
First, write down the multiplication:
[tex]\[ f(x) \cdot g(x) = (5x^2) \cdot (x^3 + 2x^2 - 5x) \][/tex]
Now distribute [tex]\( 5x^2 \)[/tex] to each term inside the parentheses:
[tex]\[ 5x^2 \cdot x^3 + 5x^2 \cdot 2x^2 + 5x^2 \cdot (-5x) \][/tex]
Now calculate each term separately:
1. [tex]\( 5x^2 \cdot x^3 = 5x^{2+3} = 5x^5 \)[/tex]
2. [tex]\( 5x^2 \cdot 2x^2 = 10x^{2+2} = 10x^4 \)[/tex]
3. [tex]\( 5x^2 \cdot (-5x) = -25x^{2+1} = -25x^3 \)[/tex]
So, combine these together:
[tex]\[ f(x) \cdot g(x) = 5x^5 + 10x^4 - 25x^3 \][/tex]
From the given choices, the correct answer is:
[tex]\[ \boxed{5x^5 + 10x^4 - 25x^3} \][/tex]
