Let f(x) = 2x+5 and g(x) = 3x^2 + 5x.
After simplifying,
(f*g)(x) =
 


To simplify \((f \cdot g)(x)\), we need to find the product of \(f(x)\) and \(g(x)\), which is given by:

\[
(f \cdot g)(x) = f(x) \cdot g(x)
\]

Given:
- \(f(x) = 2x + 5\)
- \(g(x) = 3x^2 + 5x\)

Now, multiply \(f(x)\) by \(g(x)\):

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

Apply the distributive property (FOIL):

\[
= 2x \cdot 3x^2 + 2x \cdot 5x + 5 \cdot 3x^2 + 5 \cdot 5x
\]

Simplifying each term:

\[
= 6x^3 + 10x^2 + 15x^2 + 25x
\]

Combine like terms:

\[
= 6x^3 + (10x^2 + 15x^2) + 25x
\]
\[
= 6x^3 + 25x^2 + 25x
\]

Thus, the simplified expression is:

\[
(f \cdot g)(x) = 6x^3 + 25x^2 + 25x
\]

Would you like more details or further clarifications?

Here are 5 related questions to extend the understanding:
1. How would you find \((f + g)(x)\) for the same functions?
2. What is the derivative of \((f \cdot g)(x)\)?
3. Can you compute \((f \circ g)(x)\) or \((g \circ f)(x)\) (function composition)?
4. What happens when \(x = 1\) in \((f \cdot g)(x)\)?
5. How does this multiplication change if \(f(x)\) or \(g(x)\) were higher-degree polynomials?

**Tip:** When multiplying polynomials, always group like terms (terms with the same powers) to simplify.

Let f(x) = 2x+5 and g(x) = 3x^2 + 5x. After simplifying, (f*g)(x) = ?

Learn how to multiply polynomials by simplifying (f*g)(x), where f(x) = 2x + 5 and g(x) = 3x^2 + 5x. This problem involves key algebraic concepts, including the distributive property and combining like terms, suitable for students in Grades 9-11.

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