(Assuming you mean .)
If it is reducible it must have a linear factor so just evaluate the polynomial for each value and if all are nonzero than it is irreducible.
i have others problems:
Does 144 mod 25 have an additive inverse mod 25. If yes, give it.
Does 144 mod 25 have an multiplicative inverse mod 25. If yes, give it.
I dont really understand about additive inverse and multiplicative inverse. could you help me please ?
An multiplicative inverse of 144 mod 25 is a number which you multiply to it to get 1 mod 25. x has a multiplicative inverse modulo n iff gcd(x,n)=1.
Can you answer it now? You may want to note that 144 = 19 mod 25.
What you should have said is that the multiplicative inverse of 144 (mod 25) is 4, because 144 = 19 (mod 25) and 19×4 = 76 = 75 + 1 = 1 (mod 25).