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What is $(f * g)(x)$ ? $\newline$ $f(x) = 5x$ $\newline$ $g(x) = 3x^2 - 8x$ $\newline$ 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) = 3x^2 - 8x

\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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Define Product: We have: $\newline$ $f(x) = 5x$ $\newline$ $g(x) = 3x^2 - 8x$ $\newline$ To find $(f * g)(x)$ , we need to multiply $f(x)$ by $g(x)$ . $\newline$ $(f * g)(x) = 5x * (3x^2 - 8x)$
Multiply Functions: Distribute $5x$ across the terms in $g(x)$ . $(f * g)(x) = 5x * 3x^2 - 5x * 8x$
Distribute Terms: Perform the multiplication. $\newline$ $(f * g)(x) = 15x^3 - 40x^2$
Perform Multiplication: Express your answer as a simplified polynomial. The polynomial is already in its simplest form, so no further simplification is needed.

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