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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5xf(x) = 5x\newlineg(x)=−x2−4xg(x) = -x^2 - 4x\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)=5xf(x) = 5x\newlineg(x)=−x2−4xg(x) = -x^2 - 4x\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)=5xf(x) = 5x \newlineg(x)=−x2−4xg(x) = -x^2 - 4x \newlineWhich function represents (f∗g)(x)(f * g)(x)?\newline(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)\newline(f∗g)(x)=5x∗(−x2−4x)(f * g)(x) = 5x * (-x^2 - 4x)
  3. Calculate Product: We found: \newline(f∗g)(x)=5x∗(−x2−4x)(f * g)(x) = 5x * (-x^2 - 4x) \newlineExpress your answer as a simplified polynomial or rational function.\newlineDistribute the 5x5x across the terms in g(x)g(x).\newline(f∗g)(x)=5x∗(−x2)+5x∗(−4x)(f * g)(x) = 5x * (-x^2) + 5x * (-4x)
  4. Distribute 5x5x: Simplify the expression.(f⋅g)(x)=−5x3−20x2(f \cdot g)(x) = -5x^3 - 20x^2

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