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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3xf(x) = 3x\newlineg(x)=−2x2+xg(x) = -2x^2 + x\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)=3xf(x) = 3x\newlineg(x)=−2x2+xg(x) = -2x^2 + x\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. Calculate product: We have:\newlinef(x)=3xf(x) = 3x\newlineg(x)=−2x2+xg(x) = -2x^2 + x\newlineNow, calculate the product of f(x)f(x) and g(x)g(x).\newline(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)\newline(f∗g)(x)=3x∗(−2x2+x)(f * g)(x) = 3x * (-2x^2 + x)
  3. Distribute terms: Distribute the 3x3x across the terms in g(x)g(x).
    (f∗g)(x)=3x∗(−2x2)+3x∗x(f * g)(x) = 3x * (-2x^2) + 3x * x
    (f∗g)(x)=−6x3+3x2(f * g)(x) = -6x^3 + 3x^2

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