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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5xf(x) = -5x\newlineg(x)=−2x2+5xg(x) = -2x^2 + 5x\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)=−5xf(x) = -5x\newlineg(x)=−2x2+5xg(x) = -2x^2 + 5x\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. Define functions: We have:\newlinef(x)=−5xf(x) = -5x\newlineg(x)=−2x2+5xg(x) = -2x^2 + 5x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−5x)∗(−2x2+5x)(f * g)(x) = (-5x) * (-2x^2 + 5x)
  3. Multiply functions: Distribute −5x-5x across the terms in g(x)g(x).(f∗g)(x)=(−5x)∗(−2x2)+(−5x)∗(5x)(f * g)(x) = (-5x) * (-2x^2) + (-5x) * (5x)
  4. Distribute −5x-5x: Perform the multiplication.\newline(f⋅g)(x)=10x3−25x2(f \cdot g)(x) = 10x^3 - 25x^2

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