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What is (f+g)(x)(f + g)(x)?\newlinef(x)=5xf(x) = 5x\newlineg(x)=2x2+8xg(x) = 2x^2 + 8x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f+g)(x)(f + g)(x)?\newlinef(x)=5xf(x) = 5x\newlineg(x)=2x2+8xg(x) = 2x^2 + 8x\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. Find f+gf + g: We have: \newlinef(x)=5xf(x) = 5x \newlineg(x)=2x2+8xg(x) = 2x^2 + 8x\newlineNow, we need to find (f+g)(x)(f + g)(x) by adding f(x)f(x) and g(x)g(x) together.\newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x) \newline(f+g)(x)=5x+(2x2+8x)(f + g)(x) = 5x + (2x^2 + 8x)
  3. Combine like terms: Combine like terms to simplify the expression.\newline(f+g)(x)=2x2+(5x+8x)(f + g)(x) = 2x^2 + (5x + 8x)\newline(f+g)(x)=2x2+13x(f + g)(x) = 2x^2 + 13x\newlineThis is the simplified polynomial form of (f+g)(x)(f + g)(x).

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