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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−4xf(x) = -4x\newlineg(x)=5x+2g(x) = 5x + 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)=−4xf(x) = -4x\newlineg(x)=5x+2g(x) = 5x + 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)=−4xf(x) = -4x\newlineg(x)=5x+2g(x) = 5x + 2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−4x)∗(5x+2)(f * g)(x) = (-4x) * (5x + 2)
  3. Distribute −4x-4x: Distribute −4x-4x across the terms in the parentheses.\newline(f⋅g)(x)=(−4x⋅5x)+(−4x⋅2)(f \cdot g)(x) = (-4x \cdot 5x) + (-4x \cdot 2)
  4. Perform Multiplication: Perform the multiplication.\newline(f⋅g)(x)=−20x2−8x(f \cdot g)(x) = -20x^2 - 8x

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