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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=−4x+6g(x) = -4x + 6\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)=−3x2f(x) = -3x^2\newlineg(x)=−4x+6g(x) = -4x + 6\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 product: We have:\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=−4x+6g(x) = -4x + 6\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)=(−3x2)∗(−4x+6)(f * g)(x) = (-3x^2) * (-4x + 6)
  3. Multiply functions: Distribute −3x2-3x^2 to both terms in g(x)g(x).(f∗g)(x)=(−3x2)∗(−4x)+(−3x2)∗6(f * g)(x) = (-3x^2) * (-4x) + (-3x^2) * 6
  4. Distribute terms: Perform the multiplication.\newline(f∗g)(x)=12x3−18x2(f * g)(x) = 12x^3 - 18x^2

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