Question

Which polynomial is prime? x3 + 3x2 – 2x – 6 x3 – 2x2 + 3x – 6 4x4 + 4x3 – 2x – 2 2x4 + x3 – x + 2

Answer 1

A prime polynomial is a polynomial that can't be factored.

In order to check which polynomial is prime, we need to check which polynomials could be factored.

x^3 + 3x^2 – 2x – 6 can be factored as (x+3)(x^2-2)

x^3 – 2x^2 + 3x – 6 can be factored as (x-2)(x^2+3)

4x^4 + 4x^3 – 2x – 2 can be factored as 2(x+1)(2x^3-1)

2x^4 + x^3 – x + 2 can't be factored.

Therefore, 2x^4 + x^3 – x + 2 is a prime polynomial.

Answer 2

D. 2x4+x3–x+2 is prime