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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−4xf(x) = -4x\newlineg(x)=2x2−2g(x) = 2x^2 - 2\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)=2x2−2g(x) = 2x^2 - 2\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)=−4xf(x) = -4x \newlineg(x)=2x2−2g(x) = 2x^2 - 2 \newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−4x)∗(2x2−2)(f * g)(x) = (-4x) * (2x^2 - 2)
  3. Distribute −4x-4x: Distribute −4x-4x to each term in the second function.\newline(f∗g)(x)=(−4x)∗(2x2)+(−4x)∗(−2)(f * g)(x) = (-4x) * (2x^2) + (-4x) * (-2)
  4. Perform Multiplication: Perform the multiplication.\newline(f⋅g)(x)=−8x3+8x(f \cdot g)(x) = -8x^3 + 8x
  5. Express Answer: Express your answer as a simplified polynomial.\newlineThe polynomial is already in its simplest form, so we do not need to combine any like terms.\newline(f∗g)(x)=−8x3+8x(f * g)(x) = -8x^3 + 8x

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