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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5x+6f(x) = -5x + 6\newlineg(x)=2x2g(x) = 2x^2\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)=−5x+6f(x) = -5x + 6\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. Given Functions: We have:\newlinef(x)=−5x+6f(x) = -5x + 6\newlineg(x)=2x2g(x) = 2x^2\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)=(−5x+6)∗(2x2)(f * g)(x) = (-5x + 6) * (2x^2)
  3. Calculate Product: Distribute each term in f(x)f(x) to each term in g(x)g(x) to find the product.(f∗g)(x)=(−5x∗2x2)+(6∗2x2)(f * g)(x) = (-5x * 2x^2) + (6 * 2x^2)
  4. Perform Multiplication: Perform the multiplication for each term.\newline(f∗g)(x)=−10x3+12x2(f * g)(x) = -10x^3 + 12x^2

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