Answer :
To find the product of the functions [tex]\( f(x) = 5x^2 \)[/tex] and [tex]\( g(x) = x^3 + 2x^2 - 5x \)[/tex], we need to multiply these expressions together. Here's how you can do it step by step:
1. Write down the expressions:
- [tex]\( f(x) = 5x^2 \)[/tex]
- [tex]\( g(x) = x^3 + 2x^2 - 5x \)[/tex]
2. Multiply [tex]\( f(x) \)[/tex] by each term in [tex]\( g(x) \)[/tex]:
- Multiply [tex]\( 5x^2 \)[/tex] by [tex]\( x^3 \)[/tex]:
[tex]\[
5x^2 \cdot x^3 = 5x^{2+3} = 5x^5
\][/tex]
- Multiply [tex]\( 5x^2 \)[/tex] by [tex]\( 2x^2 \)[/tex]:
[tex]\[
5x^2 \cdot 2x^2 = 10x^{2+2} = 10x^4
\][/tex]
- Multiply [tex]\( 5x^2 \)[/tex] by [tex]\( -5x \)[/tex]:
[tex]\[
5x^2 \cdot (-5x) = -25x^{2+1} = -25x^3
\][/tex]
3. Combine all results:
[tex]\[
5x^5 + 10x^4 - 25x^3
\][/tex]
So, the result of [tex]\( f(x) \cdot g(x) \)[/tex] is [tex]\( 5x^5 + 10x^4 - 25x^3 \)[/tex].
From the given answer choices, the correct one is:
[tex]\[ 5x^5 + 10x^4 - 25x^3 \][/tex]
1. Write down the expressions:
- [tex]\( f(x) = 5x^2 \)[/tex]
- [tex]\( g(x) = x^3 + 2x^2 - 5x \)[/tex]
2. Multiply [tex]\( f(x) \)[/tex] by each term in [tex]\( g(x) \)[/tex]:
- Multiply [tex]\( 5x^2 \)[/tex] by [tex]\( x^3 \)[/tex]:
[tex]\[
5x^2 \cdot x^3 = 5x^{2+3} = 5x^5
\][/tex]
- Multiply [tex]\( 5x^2 \)[/tex] by [tex]\( 2x^2 \)[/tex]:
[tex]\[
5x^2 \cdot 2x^2 = 10x^{2+2} = 10x^4
\][/tex]
- Multiply [tex]\( 5x^2 \)[/tex] by [tex]\( -5x \)[/tex]:
[tex]\[
5x^2 \cdot (-5x) = -25x^{2+1} = -25x^3
\][/tex]
3. Combine all results:
[tex]\[
5x^5 + 10x^4 - 25x^3
\][/tex]
So, the result of [tex]\( f(x) \cdot g(x) \)[/tex] is [tex]\( 5x^5 + 10x^4 - 25x^3 \)[/tex].
From the given answer choices, the correct one is:
[tex]\[ 5x^5 + 10x^4 - 25x^3 \][/tex]
