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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2xf(x) = -2x\newlineg(x)=−2x2+xg(x) = -2x^2 + x\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)=−2xf(x) = -2x\newlineg(x)=−2x2+xg(x) = -2x^2 + x\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)=−2xf(x) = -2x\newlineg(x)=−2x2+xg(x) = -2x^2 + x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−2x)∗(−2x2+x)(f * g)(x) = (-2x) * (-2x^2 + x)
  3. Multiply functions: Distribute −2x-2x across the terms in g(x)g(x).(f∗g)(x)=(−2x)∗(−2x2)+(−2x)∗x(f * g)(x) = (-2x) * (-2x^2) + (-2x) * x
  4. Distribute −2x-2x: Perform the multiplication.\newline(f⋅g)(x)=4x3−2x2(f \cdot g)(x) = 4x^3 - 2x^2

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