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

\newline

g(x) = -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 $g(x)$ . $(f * g)(x) = f(x) * g(x)$
Define $(f * g)(x)$ : We have: $\newline$ $f(x) = -3x^2 - 2x$ $\newline$ $g(x) = -5x$ $\newline$ Now, we need to multiply these two functions to find $(f * g)(x)$ .
Multiply functions: Multiply the functions. $\newline$ $(f * g)(x) = (-3x^2 - 2x) * (-5x)$ $\newline$ $(f * g)(x) = (-3x^2 * -5x) + (-2x * -5x)$ $\newline$ $(f * g)(x) = (15x^3) + (10x^2)$
Combine like terms: Combine like terms if there are any. In this case, there are no like terms to combine. $\newline$ So, the final answer is: $\newline$ $(f * g)(x) = 15x^3 + 10x^2$

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