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What is (f+g)(x)(f + g)(x)?\newlinef(x)=3x2f(x) = 3x^2\newlineg(x)=−2x2+5xg(x) = -2x^2 + 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)=3x2f(x) = 3x^2\newlineg(x)=−2x2+5xg(x) = -2x^2 + 5x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Combine like terms: (f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)\newlineWe have f(x)=3x2f(x) = 3x^2 and g(x)=−2x2+5xg(x) = -2x^2 + 5x.\newlineSo, (f+g)(x)=3x2+(−2x2+5x)(f + g)(x) = 3x^2 + (-2x^2 + 5x).
  2. Final result: Now we combine like terms.\newline(f+g)(x)=(3x2−2x2)+5x(f + g)(x) = (3x^2 - 2x^2) + 5x\newline(f+g)(x)=x2+5x(f + g)(x) = x^2 + 5x

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