Respuesta :
Answer:
[tex]x^{2} +x+1[/tex]
Step-by-step explanation:
[tex]x^{2} +x+1[/tex] is the only prime polynomial because the others can be factored.
[tex]x^{2} - x -2 \\becomes (x-2)(x+1)[/tex]
[tex]x^{2} -12x+11\\becomes (x-11)(x-1)[/tex]
[tex]x^{2} +2x-8\\becomes (x+4)(x-2)[/tex]
In between these four polynomials, x² + x + 1 is the only prime polynomial.
What is a prime polynomial?
A prime polynomial doesn't have any factor except 1 and itself.
Given,
x² + x + 1 = 1 × (x² + x + 1)
x² – x – 2 = x² - 2x + x - 2 = x(x - 2) + (x - 2) = (x - 2)(x + 1)
x² – 12x + 11 = x² – 11x - x + 11 = x(x – 11) - (x - 11) = (x - 1)(x - 11)
x² + 2x – 8 = x² + 4x – 2x - 8 = x(x+4) - 2(x+4) = (x-2)(x+4)
Therefore, x² + x + 1 is the only prime polynomial here.
Learn more about prime polynomial here: https://brainly.com/question/15562251
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