For this exercise, you are supposed to show that the polynomial $$ x^4+1 $$ is irreducible in $\mathbb{Z}_5$. However, I found that $$ (x^2+2)(x^2+3) = x^4+5x^2+6 = x^4+1. $$
Is the question wrong or am I?
Book citation: Pinter, Charles C. "A book of abstract algebra. Reprint of the second (1990) edition." (2010).