Question

Which expression is a prime polynomial?A. X^3-bx^2B. X^2-4x-12C. X^+8xy^3D. X^2-b^3

Answer 1

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.