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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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Full solution

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 f(x)f(x) to each term in g(x)g(x) to find the product.(f∗g)(x)=(−5x∗3x2)+(2∗3x2)(f * g)(x) = (-5x * 3x^2) + (2 * 3x^2)
  4. Perform Multiplication: Perform the multiplication for each term.\newline(f∗g)(x)=−15x3+6x2(f * g)(x) = -15x^3 + 6x^2

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