Homework SourseWhich of the following polynomials is not irreducible in Rx
Which of the following polynomials is not irreducible in R[x]? Question 2 options:
1) x + 2
2) x2 2
3) x2 + x + 1
4) x2 + 1
Solution
x + 2 = 0
it cannot be factorized further
x^2 - 2 = 0
(x - sqrt 2)*(x + sqrt 2) = 0
x = sqrt 2 OR x = -sqrt 2
So its not irreducible,
similarly
x^2 + x+ 1 = 0
can not be factorized further and Also,
x^2 + 1 = 0
cannot be factorized, So
Correct option is B.
![Which of the following polynomials is not irreducible in R[x]? Question 2 options: 1) x + 2 2) x2 2 3) x2 + x + 1 4) x2 + 1Solutionx + 2 = 0 it cannot be factor](/WebImages/41/which-of-the-following-polynomials-is-not-irreducible-in-rx-1126039-1761600423-0.webp "Which of the following polynomials is not irreducible in R[x]? Question 2 options: 1) x + 2 2) x2 2 3) x2 + x + 1 4) x2 + 1Solutionx + 2 = 0 it cannot be factor")
