Guys Help! thx!

Show that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x].

- Mar 29th 2012, 03:02 AMfourthShow that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x].
Guys Help! thx!

Show that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x]. - Mar 29th 2012, 04:08 AMSylvia104Re: Show that the polynomial f(x)=2x+1 has a multiplicative inverse in Z_4 [x]
$\displaystyle \left[f(x)\right]^2=(2x+1)^2=4x^2+4x+1=1$ in $\displaystyle \mathbb Z_4[x].$ So $\displaystyle f(x)$ is its own inverse in $\displaystyle \mathbb Z_4[x].$