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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=2x+3g(x) = 2x + 3\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=2x+3g(x) = 2x + 3\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)=x2f(x) = x^2 \newlineg(x)=2x+3g(x) = 2x + 3 \newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=x2∗(2x+3)(f * g)(x) = x^2 * (2x + 3)
  3. Distribute x2x^2: Distribute x2x^2 to both terms in the parentheses.\newline(f⋅g)(x)=x2⋅2x+x2⋅3(f \cdot g)(x) = x^2 \cdot 2x + x^2 \cdot 3
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=2x3+3x2(f \cdot g)(x) = 2x^3 + 3x^2
  5. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial 2x3+3x22x^3 + 3x^2 is already in its simplest form.

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