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What is $(f * g)(x)$ ? $\newline$ $f(x) = -2x^2$ $\newline$ $g(x) = 5x + 5$ $\newline$ Write your answer as a polynomial or a rational function in simplest form. $\newline$ ______

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Add and subtract functions

Full solution

Q. What is

(f * g)(x)

?

\newline

f(x) = -2x^2

\newline

g(x) = 5x + 5

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

______

Identify Formula: Identify the formula for $(f * g)(x)$ . $(f * g)(x)$ is the product of $f(x)$ and $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Given Functions: We have: $\newline$ $f(x) = -2x^2$ $\newline$ $g(x) = 5x + 5$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (-2x^2) * (5x + 5)$
Distribute Terms: Distribute $-2x^2$ to both terms in the parentheses. $\newline$ $(f \cdot g)(x) = (-2x^2 \cdot 5x) + (-2x^2 \cdot 5)$
Perform Multiplication: Perform the multiplication. $\newline$ $(f * g)(x) = -10x^3 - 10x^2$
Final Simplified Form: There are no like terms to combine, so this is the final simplified form of the polynomial.

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Question

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