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

Please answer the following questions about arithmetic in this field.

a$)$ If $p(x)=x^3+x+1,$ what is the corresponding hexadecimal representation? Please prepend an $"0x"$ on your answer and use lowercase letters $($if letters occur$).$

b$)$ If $p(x)=x^3,$ what is the corresponding hexadecimal representation? Please prepend an $"0$x$"$ on your answer and use lowercase letters $($if letters occur$).$

c$)$ Consider the hex byte $0x15.$ What is the corresponding element of $GF(256)($as a polynomial$)?$

d$)$ Consider the hex byte $0xe.$ What is the corresponding element of GF$(256)($as a polynomial$)?$