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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x+5f(x) = 2x + 5\newlineg(x)=−2x2g(x) = -2x^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)=2x+5f(x) = 2x + 5\newlineg(x)=−2x2g(x) = -2x^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. Calculate Product: We have:\newlinef(x)=2x+5f(x) = 2x + 5\newlineg(x)=−2x2g(x) = -2x^2\newlineNow, calculate the product of f(x)f(x) and g(x)g(x).\newline(f∗g)(x)=(2x+5)∗(−2x2)(f * g)(x) = (2x + 5) * (-2x^2)
  3. Distribute Terms: Distribute −2x2-2x^2 to each term in the binomial (2x+5)(2x + 5).\newline(f∗g)(x)=−2x2∗2x+(−2x2)∗5(f * g)(x) = -2x^2 * 2x + (-2x^2) * 5
  4. Perform Multiplication: Perform the multiplication for each term.\newline(f∗g)(x)=−4x3−10x2(f * g)(x) = -4x^3 - 10x^2
  5. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial −4x3−10x2-4x^3 - 10x^2 is already in its simplest form.

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