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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+2f(x) = 3x + 2\newlineg(x)=−2x2g(x) = -2x^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)=3x+2f(x) = 3x + 2\newlineg(x)=−2x2g(x) = -2x^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)=3x+2f(x) = 3x + 2\newlineg(x)=−2x2g(x) = -2x^2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(3x+2)∗(−2x2)(f * g)(x) = (3x + 2) * (-2x^2)
  3. Distribute Terms: Distribute the terms of f(x)f(x) across the terms of g(x)g(x) to find the product.(f∗g)(x)=3x∗(−2x2)+2∗(−2x2)(f * g)(x) = 3x * (-2x^2) + 2 * (-2x^2)
  4. Perform Multiplication: Perform the multiplication for each term.\newline(f⋅g)(x)=−6x3+(−4x2)(f \cdot g)(x) = -6x^3 + (-4x^2)
  5. Combine Like Terms: Combine like terms if there are any. In this case, there are no like terms to combine.\newlineSo, the expression is already simplified.\newline(f∗g)(x)=−6x3−4x2(f * g)(x) = -6x^3 - 4x^2

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