Question

select the correct answer. which expression is a prime polynomial? \\(\bigcirc\\) a. \\(x^3 - 1\\) \\(\bigcirc\\) b. \\(x^2 + 1\\) \\(\bigcirc\\) c. \\(x^3 + 1\\) \\(\bigcirc\\) d. \\(x^2 - 1\\)

Explanation:

Step1: Factor Option A

$x^3 - 1=(x-1)(x^2+x+1)$

Step2: Check Option B irreducibility

$x^2+1$ has no real roots, cannot be factored into linear polynomials with real coefficients.

Step3: Factor Option C

$x^3 + 1=(x+1)(x^2-x+1)$

Step4: Factor Option D

$x^2 - 1=(x-1)(x+1)$

Answer:

B. $x^2 + 1$