Question

which expression is a prime polynomial?
a. $x^3 - 1$
b. $x^2 + 1$
c. $x^3 + 1$
d. $x^2 - 1$

Explanation:

Step1: Factor Option A

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

Step2: Check Option B

$x^2 + 1$ has no real factors.

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. $x^2 + 1$