Two polynomials f (x) and g(x) are congruent modulo a polynomial q(x) if and only if f (x) - g(x) is a multiple of q(x), in which case we write
Evaluate
x4 + x + 1mod
x2 + 4x + 5
= -23x - 54
To verify this calculation, note the following.
Polynomials + Divide
= x2 -4x + 11 +
This result implies that indeed
x4 + x + 1mod
x2 + 4x + 5
= - 23x - 54.