To solve for the rational zeros of the function [tex]\( f(x) = x^4 + x^3 - 15x^2 - 13x + 26 \)[/tex], we need to identify the rational solutions to the equation [tex]\( f(x) = 0 \)[/tex].
Step 1: State the polynomial function.
[tex]\[
f(x) = x^4 + x^3 - 15x^2 - 13x + 26
\][/tex]
Step 2: Identify possible rational zeros.
According to the Rational Root Theorem, any possible rational root, [tex]\( \frac{p}{q} \)[/tex], of the polynomial equation must be a factor of the constant term (26) divided by a factor of the leading coefficient (1). The factors of 26 are [tex]\( \pm 1, \pm 2, \pm 13, \pm 26 \)[/tex]. Since the leading coefficient is 1, each of these is a potential rational zero.
Step 3: Test the possible rational zeros.
However, instead of trial and error, it's more efficient to observe the result:
Step 4: List the rational zeros.
The rational zeros of the polynomial function [tex]\( f(x) = x^4 + x^3 - 15x^2 - 13x + 26 \)[/tex] are:
[tex]\[
-2, \ 1
\][/tex]
Therefore, the correct choice is:
A. The rational zero(s) is/are [tex]\(\boxed{-2, \ 1}\)[/tex].
