Homework SourseHow many elements are there in the field Z5XXSolutionWe know
How many elements are there in the field Z_5[X]X/<x^3-2x^2-1>?
Solution
We know that for a field Zp[x]/<f(x)>, if p is a prime number and degree of f(x) is n, then there are pn elements in the field.
Comparing our question Zp[x]/<x^3-2x^2-1> to Zp[x]/<f(x)>, we get p = 5 and n=3
Therefore, number of elements = pn = (5)^3 = 125
![How many elements are there in the field Z_5[X]X/<x^3-2x^2-1>?SolutionWe know that for a field Zp[x]/<f(x)>, if p is a prime number and degree of f(](/WebImages/3/how-many-elements-are-there-in-the-field-z5xxsolutionwe-know-976220-1761500787-0.webp "How many elements are there in the field Z_5[X]X/<x^3-2x^2-1>?SolutionWe know that for a field Zp[x]/<f(x)>, if p is a prime number and degree of f(")
