## Multiplicity of a root

Determine the multiplicity

• #### Variant 1

of the root 1 in the polynomial $$x^4+2x^3+x^2+3x+3$$ over $$\mathbb Z_5$$.

• #### Variant 2

the root 6 in the polynomial $$x^4+3x^3+6x^2+3x+6$$ over $$\mathbb Z_7$$.

• #### Variant 3

the root 1 in the polynomial $$x^4+x^3+2x+2$$ over $$\mathbb Z_3$$.