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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=−x+4g(x) = -x + 4\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)=−x2f(x) = -x^2\newlineg(x)=−x+4g(x) = -x + 4\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. Calculate product: We have:\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=−x+4g(x) = -x + 4\newlineNow, calculate the product of f(x)f(x) and g(x)g(x).\newline(f∗g)(x)=(−x2)∗(−x+4)(f * g)(x) = (-x^2) * (-x + 4)
  3. Distribute terms: Distribute −x2-x^2 across the terms in the parentheses.\newline(f⋅g)(x)=(−x2)⋅(−x)+(−x2)⋅4(f \cdot g)(x) = (-x^2) \cdot (-x) + (-x^2) \cdot 4
  4. Perform multiplication: Perform the multiplication. (f⋅g)(x)=x3−4x2(f \cdot g)(x) = x^3 - 4x^2

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