# Factoring expression with rational powers

To any great Mathematica-matician. Why Mathematica can’t factor this

Factor[-1+x^(2/3)]


I know that Factor mainly targets polynomials but in the "Generalization" section of the help page, there is a quite similar example:

Factor[x^(2/3 s) + 2 x^s + 1]
(* (1 + x^(s/3)) (1 - x^(s/3) + 2 x^(2 s/3)) *)


I would expect it to handle my case as well and that it gives a result like this one:

(x^(1/3)-1)*(x^(1/3)+1)

• What result would you expect from it? – MarcoB May 25 '18 at 16:03
• It's not quite clear what result you expect as this is not a polynomial. Factor works with polynomials. – Szabolcs May 25 '18 at 16:06
• Wow, so quick. I will study this answer. I think is fine. Thank you Akku14. – Sanmuten May 25 '18 at 16:38
• Why is the expected result not (x^(1/6)-1)*(x^(1/6)+1)*(x^(1/3)+1)? – Daniel Lichtblau May 26 '18 at 16:04
• I will vote to close this because it a simple mistake. The wrong assumption you made is that your function is a polynomial in x which it is not: PolynomialQ[-1 + x^(2/3), x]. The reference page of Factor clearly says that it factors polynomials. With @Akku's answer you have a good start to dig deeper but in its current form, the question makes no sense. – halirutan May 26 '18 at 22:51

-1 + x^(2/3) // ComplexExpand[#, TargetFunctions -> {Re, Im}] & //

• Surprisingly your method also works even for very large rational exponents such as 128/173 – yarchik May 27 '18 at 4:49