Use the
rational Zero Test to list all possible rational zeroes of f(x)=5x^{4}-x^{3}+4x^{2}-x-2.

(order from least to greatest and keep all non-whole number answers in fraction form)

x= , , , , , , ,

Using the Rational Zero test, we know that all Rational Zeros of the function must

have the form p/q where p and q have no common factors (other than 1) and

p= a factor of the constant term and q= factor of the leading coefficient.

The constant term here = -2; the leading coefficient=6

All factors of -2: -2, -1, 1, 2

All factors of 5: -5, -1, 1, 5

Therefore all possible rational zeroes are combinations of these numbers in fraction form:

-2/-5, -2/-1, -2/1, -2/5, -1/-5, -1/-1, -1/1, -1/5, 1/-5, 1/-1, 1/1, 1/5, 2/-5, 2/-1, 2/1, 2/5 (…eliminating all the redundant ones)

=-2, -1, -2/5, -1/5, 1/5, 2/5, 1, 2