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.
In this exercise we have to use the knowledge of prime polynomials to find what cannot be factored, so we have;
A) Can be factored.
B) Can be factored.
C) Can be factored.
D) Can't be factored.
Is a base form of a polynomial in other words is a polynomial that can't be factored.
So we have to:
A) [tex]x^3 + 3x^2 - 2x - 6 =(x+3)(x^2-2)[/tex]
B)[tex]x^3 - 2x^2 + 3x - 6=(x-2)(x^2+3)[/tex]
C)[tex]4x^4 + 4x^3- 2x - 2= 2(x+1)(2x^3-1)[/tex]
D)[tex]2x^4 + x^3 - x + 2[/tex]
See more about prime polynomials at brainly.com/question/17822016
