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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−4xf(x) = -4x\newlineg(x)=3x2−6xg(x) = 3x^2 - 6x\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)=3x2−6xg(x) = 3x^2 - 6x\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)=3x2−6xg(x) = 3x^2 - 6x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−4x)∗(3x2−6x)(f * g)(x) = (-4x) * (3x^2 - 6x)
  3. Distribute −4x-4x: Distribute −4x-4x to each term in g(x)g(x).(f∗g)(x)=(−4x∗3x2)+(−4x∗−6x)(f * g)(x) = (-4x * 3x^2) + (-4x * -6x)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=−12x3+24x2(f \cdot g)(x) = -12x^3 + 24x^2
  5. Express Answer: Express your answer as a simplified polynomial.\newlineThe polynomial is already in its simplest form, so we are done.\newline(f∗g)(x)=−12x3+24x2(f * g)(x) = -12x^3 + 24x^2

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