I know how to solve this question by choosing numbers, but if wanna do that algebraically can’t I eliminate x from both sides and on one side I would have x^2 -1 and on the other side I would have x^2, and then since x^2 is always positive I could compare -1 vs 0 and choose quantity B?
I know the answer is wrong but I’m wondering what goes wrong with the logic?

Subtracting x^3 from both sides.
New A : -x
NEW B : 0

Now if x is postive A will be negative hence quantity B is bigger. ( For ex : x = 1 , -(1) = -1 ; -1<0 )
Now if x is negative A will be positive hence quantity A is bigger. ( For ex : x = -1 , -(-1) = 1 ; 1>0 )
Now if x is 0 the answer will be C.

To answer the question why you cannot eliminate x is because what if x is 0 you cannot divide by 0. I’m not sure if this logic is entirely correct.