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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x2+4xf(x) = -x^2 + 4x\newlineg(x)=3xg(x) = 3x\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)=−x2+4xf(x) = -x^2 + 4x\newlineg(x)=3xg(x) = 3x\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. Given functions: We have:\newlinef(x)=−x2+4xf(x) = -x^2 + 4x\newlineg(x)=3xg(x) = 3x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−x2+4x)∗(3x)(f * g)(x) = (-x^2 + 4x) * (3x)
  3. Multiply functions: Distribute 3x3x to each term in the polynomial −x2+4x-x^2 + 4x. \newline(f∗g)(x)=(−x2∗3x)+(4x∗3x)(f * g)(x) = (-x^2 * 3x) + (4x * 3x)
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=−3x3+12x2(f * g)(x) = -3x^3 + 12x^2
  5. Perform multiplication: Express your answer as a simplified polynomial.\newlineThe polynomial −3x3+12x2-3x^3 + 12x^2 is already in its simplest form.

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