Question
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.
Answer all four of the following questions:
Factor the denominator completely. Show your handwritten work and explain how you got your answer.
Answers
GPT 3.5
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).
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).