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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=−3x+6g(x) = -3x + 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)=x2f(x) = x^2\newlineg(x)=−3x+6g(x) = -3x + 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 Functions: We have:\newlinef(x)=x2f(x) = x^2\newlineg(x)=−3x+6g(x) = -3x + 6\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=x2∗(−3x+6)(f * g)(x) = x^2 * (-3x + 6)
  3. Multiply Functions: Distribute x2x^2 to each term in g(x)g(x).(f∗g)(x)=x2∗(−3x)+x2∗6(f * g)(x) = x^2 * (-3x) + x^2 * 6
  4. Distribute Terms: Perform the multiplication.\newline(f∗g)(x)=−3x3+6x2(f * g)(x) = -3x^3 + 6x^2
  5. Perform Multiplication: Express your answer as a simplified polynomial.\newlineThe polynomial −3x3+6x2-3x^3 + 6x^2 is already in its simplest form.

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