List the potential rational zeros of the polynomial function. Do not find the zeros.

Question

f(x) = 11x³ - x² + 5.

Answer 1

Factors of the constant term/factors of the leading term

Factors of 5 : ±1, ±5

Factors of 11: ±1, ±11

±1/1, ±1/11, ±5/1, ±5/11

±1, ±1/11, ±5, ±5/11

Answer 2

Hi Steven L.,

It's unclear what listing as opposed to solving entails. I suggest you look up the general solution for cubic equations -- it's quite involved, compared to the simple quadratic one -- and look at the types of roots generated, usually either 3 real or 1 real and 2 complex, if I recall (or some degeneracy of these). There is a quantity analogous to the determinant of a quadratic (b^2-4ac) that steers you to these. Perhaps that is what your questioner is seeking. However, if you go to all that trouble, you might as well just solve, if only to look at the multi-stage-radical expressions entailed. Note that you have a form without a first-degree term or coefficient; if you are ambitious you may be able to factor into (ax^2 + bx + c) and (dx+e) terms?

-- Cheers, --Mr. d.