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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4x+1f(x) = 4x + 1\newlineg(x)=−4xg(x) = -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)=4x+1f(x) = 4x + 1\newlineg(x)=−4xg(x) = -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. Calculate Product: We have:\newlinef(x)=4x+1f(x) = 4x + 1\newlineg(x)=−4xg(x) = -4x\newlineNow, calculate the product of f(x)f(x) and g(x)g(x).\newline(f∗g)(x)=(4x+1)∗(−4x)(f * g)(x) = (4x + 1) * (-4x)
  3. Distribute Terms: Distribute the terms to find the product.\newline(f∗g)(x)=4x∗(−4x)+1∗(−4x)(f * g)(x) = 4x * (-4x) + 1 * (-4x)\newline(f∗g)(x)=−16x2−4x(f * g)(x) = -16x^2 - 4x
  4. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial −16x2−4x-16x^2 - 4x is already in its simplest form.

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