Answer:
The correct answer is x^2 + x + 1.
Step-by-step explanation:
A prime polynomial is one that cannot be factored. To solve this problem, we can use the process of elimination by eliminating all answer choices that can be factored.
x^2 - x - 2 = (x - 2)*(x + 1)
x^2 - 12x + 11 = (x - 11)*(x - 1)
x^2 + 2x - 8 = (x + 4)*(x - 2)
Since we cannot factor x^2 + x + 1, and we can factor all of the other answer choices, we know that x^2 + x + 1 is the answer.
Hope this helps!
