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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−4x+2f(x) = -4x + 2\newlineg(x)=−x2g(x) = -x^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)=−4x+2f(x) = -4x + 2\newlineg(x)=−x2g(x) = -x^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. Define functions: We have:\newlinef(x)=−4x+2f(x) = -4x + 2\newlineg(x)=−x2g(x) = -x^2\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−4x+2)∗(−x2)(f * g)(x) = (-4x + 2) * (-x^2)
  3. Multiply functions: Distribute each term in f(x)f(x) to each term in g(x)g(x).(f∗g)(x)=(−4x)(−x2)+(2)(−x2)(f * g)(x) = (-4x)(-x^2) + (2)(-x^2)
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=4x3−2x2(f * g)(x) = 4x^3 - 2x^2

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