Which one is remainder theorem

How many polynomials are there of degree

 $n$  in  $Z_{11}\left[x\right]$  ?

Let $f\left(x\right),g\left(x\right)\in Z_7\left(x\right)$  where $f\left(x\right)=2x^2+x+2$  and $g\left(x\right)=6x+1$  find  $f\left(x\right)+g\left(x\right)$  

If $f\left(x\right)=x^2+1,\ g\left(x\right)=x^4+x^3+x^2+x+1,\ f\left(x\right),\ g\left(x\right)\in Z_2\left[x\right],$  

find $r\left(x\right)$  

If $f\left(x\right),\ g\left(x\right)\in Q\left[x\right],\ f\left(x\right)=x^8+7x^5-4x^4+3x^3+5x^2-4,\ g\left(x\right)=x-3$ 

find the remainder when $f\left(x\right)$  is divided by $g\left(x\right)$  

If $f\left(x\right)=x^3+5x^2+2x+6,\ f\left(x\right)\in Z_7\left[x\right]$  , then determine all of the roots in $Z_7$  and write $f\left(x\right)$  as a product of first degree polynomials.

How many units are there in the ring $Z_5\left[x\right]$ 

Let $ab=ba=u$  , then  $b$  is called

Every non-zero polynomial of degree is less than or equal to 1 is called

When the polynomial is called monic

If $\left|F\right|=q$  and degree $s\left(x\right)=n$  , then $\frac{F\left[x\right]}{s\left(x\right)}$  contains

What is the degree of $2x^3+x+1$  

How many monic polynomials in $Z_7\left[x\right]$  have degree 4

What is the gcd of $f\left(x\right)=x^2+x-2,\ g\left(x\right)=x^5-x^4+x^3+x^2-x-1$  

Check whether $S\left(x\right)=x^2+1$  is reducible or not in $Z_2\left[x\right]$  

Let $s\left(x\right)=x^4+x^3+1\in Z_2\left[x\right]$  What is the order of the field $\frac{Z_2\left[x\right]}{S\left(x\right)}?$  

How many elements in $\frac{Z_p\left[x\right]}{s\left(x\right)}$  generate the multiplicative group of non-zero elements of this field?

Give the characteristic for $Z_{10}\left[x\right]$  

Construct a finite field of 27 elements