Question

Let I= (x2 +2) in Z7 [x] , and let R be the factor ring Z7...

Let I= (x2 +2) in Z7 [x] , and let R be the factor ring Z7 [x] / I.

a) Prove that every element of R can be written in the form f + I where f is an element of Z7 [x] and deg(f0< or =2 or f=0. That is,

R={ f + I : f in Z7 [x] and (deg (f) , or=2 or f=0)}

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