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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=2x+5g(x) = 2x + 5\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)=−3x2f(x) = -3x^2\newlineg(x)=2x+5g(x) = 2x + 5\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. Find f∗gf * g: We have:\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=2x+5g(x) = 2x + 5\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)=(−3x2)∗(2x+5)(f * g)(x) = (-3x^2) * (2x + 5)
  3. Distribute −3x2-3x^2: Distribute −3x2-3x^2 to both terms in g(x)g(x).(f∗g)(x)=(−3x2∗2x)+(−3x2∗5)(f * g)(x) = (-3x^2 * 2x) + (-3x^2 * 5)
  4. Perform Multiplication: Perform the multiplication. (f∗g)(x)=−6x3−15x2(f * g)(x) = -6x^3 - 15x^2

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