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At least one of the answers above is NOT correct.

$(1$ point$)$ This question concerns the field $GF(256).$ The modulus is $P(x)=x^8+x^4+x^3+x+1.$

For computing inverses in this field, you should use the table in the textbook.

Please answer the following questions about arithmetic in this field.

a$)$ If $p(x)=x^7+x^6+x^4+x^3+x+1,$ and $q(x)=x^4+x^2+x,$ what is $p\frac{x}{q}(x)?$

b$)$ If $p(x)=x^6+x^5+x^3+x^2+x,$ and $q(x)=x^7+x^5+1,$ what is $p\frac{x}{q}(x)?$