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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−x2−10xf(x) = -x^2 - 10x\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)=−x2−10xf(x) = -x^2 - 10x\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 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. Calculate Sum: We have:\newlinef(x)=−x2−10xf(x) = -x^2 - 10x\newlineg(x)=2x2g(x) = 2x^2\newlineNow, let's find (f+g)(x)(f + g)(x) by adding f(x)f(x) and g(x)g(x) together.\newline(f+g)(x)=(−x2−10x)+(2x2)(f + g)(x) = (-x^2 - 10x) + (2x^2)
  3. Combine Like Terms: Combine like terms.\newline(f+g)(x)=−x2+2x2−10x(f + g)(x) = -x^2 + 2x^2 - 10x\newline(f+g)(x)=(2x2−x2)−10x(f + g)(x) = (2x^2 - x^2) - 10x\newline(f+g)(x)=x2−10x(f + g)(x) = x^2 - 10x

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