Solution Found!
Show that 4x2 + 6x + 3 is a unit in Z8[x].
Chapter 14, Problem 41SE(choose chapter or problem)
QUESTION:
Show that \(4 x^{2}+6 x+3\) is a unit in \(Z_{8}[x]\).
Questions & Answers
QUESTION:
Show that \(4 x^{2}+6 x+3\) is a unit in \(Z_{8}[x]\).
ANSWER:
Step 1 of 3
Recall that an element of a ring is a unit if its inverse exists.
Find the inverse of \(4 x^{2}+6 x+3\).
Here, in 4 x^{2}+6 x+3 the constant term is 3. The inverse of 3 in \(Z_8\) is 3 as
\(3 \cdot 3=9 \bmod 8=1 \bmod 8\)
Therefore, the inverse of \(4 x^{2}+6 x+3\) should have 3 as a constant term.