Question

Identify a cubic polynomial with integer coefficients that has 2^(1/3) + 4^(1/3) as a root.

I tried solving it but my polynomial ended up having non-integer coefficients. I just can't think of a way to find it so that my polynomial has integer coefficients. Help, please!

Answer 1

recall that 2+4 = (∛2^3 + ∛4^3) = (∛2 + ∛4)(∛4 - ∛8 + ∛16)
See what you can do with that. You might try using perfect cubes to see what's going on.

Answer 2

Thanks for the reply.
I hadn't considered the idea of using perfect cubes. How would I use perfect cubes, though? I'm still confused.

Answer 3

Never mind, I found an answer. Thanks for the help though!