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What is (f+g)(x)(f + g)(x)?\newlinef(x)=3x2f(x) = 3x^2\newlineg(x)=3x2−6xg(x) = 3x^2 - 6x\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)=3x2−6xg(x) = 3x^2 - 6x\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)=3x2f(x) = 3x^2\newlineg(x)=3x2−6xg(x) = 3x^2 - 6x\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)=f(x)+g(x)(f + g)(x) = f(x) + g(x)\newline(f+g)(x)=3x2+(3x2−6x)(f + g)(x) = 3x^2 + (3x^2 - 6x)
  3. Combine Like Terms: Combine like terms.\newline(f+g)(x)=3x2+3x2−6x(f + g)(x) = 3x^2 + 3x^2 - 6x\newline(f+g)(x)=6x2−6x(f + g)(x) = 6x^2 - 6x\newlineThis is the simplest form of the polynomial.

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