For the rational function f(x)=x-1/4x^2-4
Answer all four of the following questions:
Factor the denominator completely. Show your handwritten work and explain how you got your answer.
To factor the denominator of the rational function f(x), we need to express it as a product of binomials.
The denominator is 4x^2 - 4. To factor it, we can first factor out the greatest common factor, which is 4. This gives us:
4(x^2 - 1)
Now, we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = x and b = 1. So, applying the formula, we have:
4(x + 1)(x - 1)
Therefore, the denominator of the rational function f(x) is completely factored as 4(x + 1)(x - 1).