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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−4xf(x) = -4x\newlineg(x)=−3x+3g(x) = -3x + 3\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)=−4xf(x) = -4x\newlineg(x)=−3x+3g(x) = -3x + 3\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. Multiply Functions: We have:\newlinef(x)=−4xf(x) = -4x\newlineg(x)=−3x+3g(x) = -3x + 3\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−4x)∗(−3x+3)(f * g)(x) = (-4x) * (-3x + 3)
  3. Distribute −4x-4x: Distribute −4x-4x to both terms in the second function.\newline(f∗g)(x)=(−4x)∗(−3x)+(−4x)∗3(f * g)(x) = (-4x) * (-3x) + (-4x) * 3
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=12x2−12x(f \cdot g)(x) = 12x^2 - 12x
  5. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial 12x2−12x12x^2 - 12x is already in its simplest form.

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