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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x2−3xf(x) = -x^2 - 3x\newlineg(x)=5xg(x) = 5x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x2−3xf(x) = -x^2 - 3x\newlineg(x)=5xg(x) = 5x\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. Given functions: We have:\newlinef(x)=−x2−3xf(x) = -x^2 - 3x\newlineg(x)=5xg(x) = 5x\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)=(−x2−3x)∗(5x)(f * g)(x) = (-x^2 - 3x) * (5x)
  3. Multiply functions: Distribute 5x5x to each term in the polynomial (−x2−3x)(-x^2 - 3x).
    (f∗g)(x)=(−x2∗5x)+(−3x∗5x)(f * g)(x) = (-x^2 * 5x) + (-3x * 5x)
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=−5x3−15x2(f * g)(x) = -5x^3 - 15x^2

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