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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−2x2−5xf(x) = -2x^2 - 5x\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)=−2x2−5xf(x) = -2x^2 - 5x\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 sum 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. Add Functions: We have:\newlinef(x)=−2x2−5xf(x) = -2x^2 - 5x\newlineg(x)=−5xg(x) = -5x\newlineNow, we need to add these two functions to find (f+g)(x)(f + g)(x).\newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)\newline(f+g)(x)=(−2x2−5x)+(−5x)(f + g)(x) = (-2x^2 - 5x) + (-5x)
  3. Combine Like Terms: Combine like terms.\newline(f+g)(x)=−2x2−5x−5x(f + g)(x) = -2x^2 - 5x - 5x\newline(f+g)(x)=−2x2−10x(f + g)(x) = -2x^2 - 10x\newlineThis is the simplified form of the polynomial.

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