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What is $(f * g)(x)$ ? $\newline$ $f(x) = -5x$ $\newline$ $g(x) = 2x^2 - 5x$ $\newline$ 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) = -5x

\newline

g(x) = 2x^2 - 5x

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Multiply functions: We have: $\newline$ $f(x) = -5x$ $\newline$ $g(x) = 2x^2 - 5x$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ . $\newline$ $(f * g)(x) = (-5x) * (2x^2 - 5x)$
Distribute $-5x$ : Distribute $-5x$ across the terms in $g(x)$ . $(f \cdot g)(x) = (-5x) \cdot (2x^2) + (-5x) \cdot (-5x)$
Perform multiplication: Perform the multiplication. $\newline$ $(f \cdot g)(x) = -10x^3 + 25x^2$
Express as polynomial: Express your answer as a simplified polynomial. $\newline$ The polynomial is already in its simplest form, so we are done. $\newline$ $(f * g)(x) = -10x^3 + 25x^2$

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