Answer :
The possible rational zeros for the function f(x) = x^5 - 4x^2 + 4x + 35 are: ±1/1, ±5/1, ±7/1, ±35/1, ±1/1, ±5/1, ±7/1, and ±35/1. The Rational Zero Theorem is a method that helps us find possible rational zeros of a polynomial function. To find the possible rational zeros for the function f(x) = x^5 - 4x^2 + 4x + 35, we can use the following steps:
Step 1: Identify the factors of the constant term (35). In this case, the factors of 35 are ±1, ±5, ±7, and ±35.
Step 2: Identify the factors of the leading coefficient (1). In this case, the factors of 1 are ±1.
Step 3: Generate a list of possible rational zeros by taking the ratio of the factors of the constant term to the factors of the leading coefficient. This gives us the following possible rational zeros: ±1/1, ±5/1, ±7/1, ±35/1, ±1/1, ±5/1, ±7/1, and ±35/1.
Step 4: Simplify the fractions and check if they are valid zeros by substituting them into the original function. For example, if we simplify ±5/1 to ±5, we can substitute these values into f(x) = x^5 - 4x^2 + 4x + 35 and check if the result is zero. Repeat this process for all the other possible rational zeros.
Please note that the Rational Zero Theorem provides a list of all possible rational zeros, but not all of them will necessarily be valid zeros for the function.
To know more about Rational Zero Theorem, refer to
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