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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+5f(x) = 3x + 5\newlineg(x)=−x2g(x) = -x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+5f(x) = 3x + 5\newlineg(x)=−x2g(x) = -x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify Formula: Identify the formula for (f∗g)(x)(f * g)(x).(f∗g)(x)(f * g)(x) is the product of f(x)f(x) and g(x)g(x).(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)
  2. Define Functions: We have:\newlinef(x)=3x+5f(x) = 3x + 5\newlineg(x)=−x2g(x) = -x^2\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(3x+5)∗(−x2)(f * g)(x) = (3x + 5) * (-x^2)
  3. Multiply Functions: Distribute −x2-x^2 to each term in the polynomial 3x+53x + 5.
    (f∗g)(x)=3x∗(−x2)+5∗(−x2)(f * g)(x) = 3x * (-x^2) + 5 * (-x^2)
  4. Distribute Terms: Perform the multiplication for each term.\newline(f∗g)(x)=−3x3−5x2(f * g)(x) = -3x^3 - 5x^2

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