# How do you solve #x^6 - 9x^3 +8=0#?

##### 1 Answer

This polynomial is quadratic in

So

#### Explanation:

...using the difference of cubes identity (twice):

Neither of the remaining quadratic factors have linear factors with real coefficients. You can find the discriminant of each to prove that for yourself, or you can factor them using complex numbers as follows:

Where

is the primitive complex cube root of unity.

graph{x^6-9x^3+8 [-40.17, 39.83, -18.08, 21.92]}