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What is (f−g)(x)(f - g)(x)?\newlinef(x)=5x+5f(x) = 5x + 5\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)=5x+5f(x) = 5x + 5\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). The correct formula is (f−g)(x)=f(x)−g(x)(f - g)(x) = f(x) - g(x).
  2. Substitute Values: We have f(x)=5x+5f(x) = 5x + 5 and g(x)=−2x2g(x) = -2x^2. Substitute these values into the formula to get (f−g)(x)=(5x+5)−(−2x2)(f - g)(x) = (5x + 5) - (-2x^2).
  3. Simplify Equation: Simplify the equation (f−g)(x)=(5x+5)−(−2x2)(f - g)(x) = (5x + 5) - (-2x^2) to find (f−g)(x)(f - g)(x).
    (f−g)(x)=5x+5+2x2(f - g)(x) = 5x + 5 + 2x^2
    Note that we have removed the minus sign in front of −2x2-2x^2 by distributing the subtraction across the polynomial, effectively changing the sign of each term in g(x)g(x).
  4. Rearrange Terms: Rearrange the terms in descending order of the power of xx to write the polynomial in standard form.(f−g)(x)=2x2+5x+5(f - g)(x) = 2x^2 + 5x + 5

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