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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x2−7xf(x) = -2x^2 - 7x\newlineg(x)=5xg(x) = 5x\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)=−2x2−7xf(x) = -2x^2 - 7x\newlineg(x)=5xg(x) = 5x\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)=−2x2−7xf(x) = -2x^2 - 7x\newlineg(x)=5xg(x) = 5x\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−2x2−7x)∗(5x)(f * g)(x) = (-2x^2 - 7x) * (5x)
  3. Distribute Terms: Distribute 5x5x to each term in f(x)f(x).$(f∗g)(x)=(−2x2∗5x)+(−7x∗5x)\$(f * g)(x) = (-2x^2 * 5x) + (-7x * 5x)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=−10x3−35x2(f \cdot g)(x) = -10x^3 - 35x^2

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