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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5x+2f(x) = 5x + 2\newlineg(x)=−3x2g(x) = -3x^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)=5x+2f(x) = 5x + 2\newlineg(x)=−3x2g(x) = -3x^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)=5x+2f(x) = 5x + 2\newlineg(x)=−3x2g(x) = -3x^2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(5x+2)∗(−3x2)(f * g)(x) = (5x + 2) * (-3x^2)
  3. Distribute terms: Distribute each term in the first polynomial over the second polynomial.\newline(f⋅g)(x)=5x⋅(−3x2)+2⋅(−3x2)(f \cdot g)(x) = 5x \cdot (-3x^2) + 2 \cdot (-3x^2)
  4. Perform multiplication: Perform the multiplication for each term.\newline(f⋅g)(x)=−15x3−6x2(f \cdot g)(x) = -15x^3 - 6x^2

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