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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x2−3xf(x) = -2x^2 - 3x\newlineg(x)=4xg(x) = 4x\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)=−2x2−3xf(x) = -2x^2 - 3x\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. Define (f∗g)(x)(f * g)(x): We have:\newlinef(x)=−2x2−3xf(x) = -2x^2 - 3x\newlineg(x)=4xg(x) = 4x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).
  3. Given functions: Multiply the functions.\newline(f∗g)(x)=(−2x2−3x)∗(4x)(f * g)(x) = (-2x^2 - 3x) * (4x)\newline(f∗g)(x)=−2x2∗4x+(−3x)∗4x(f * g)(x) = -2x^2 * 4x + (-3x) * 4x\newline(f∗g)(x)=−8x3−12x2(f * g)(x) = -8x^3 - 12x^2

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