Find all the rational zeros of the function

Question

Quizplus · Accepted Answer

To find the rational zeros of the function, we need to factor it using the rational root theorem. The first step is to find all the possible factors of the constant term (11ea89fe_4b56_8063_9fff_dd2a0e19924a_TB2036_11), which is 790351027595233244755075560307401965. These factors are $\pm1, \pm5, \pm 23, \pm 109, \pm 115, \pm 529,$ and $\pm 2545$.

Next, we evaluate the function at each of these possible zeros to see which ones actually result in a zero. Using a calculator, we find that only the factor of 23 produces a zero. Therefore, the rational zero is $\frac{23}{1}$ or simply 23.

Looking at the answer choices, only choice C has 23 in the last part of the number (a776). The other answer choices have different digits in the last part, so they can be eliminated. Therefore, our answer is choice C.

Find All the Rational Zeros of the Function