A prime polynomial is one that can only be divided by itself and 1. Let's check it option.
A. x³-bx²
This polynomial can be divided by itself, 1, x and x². So it can't be prime.
B. x²-4x-12
This polynomial represents the standard form of a second order polynomial. This means that it is a parabolla. A polynomial of this form can be divided by (x-a) where "a" is the value of its roots. So it can't be prime.
C. x+8xy³
This polynomial can be divided by x, 1 and itself, therefore it can't be a prime.
D. x²-b³
This polynomial can only be divided by 1 and itself. So this is the correct answer.
