$(1$ point$)$ This question concerns the field $GF(16).$ The modulus is $P(x)=x^4+x+1.$

Please answer the following questions about arithmetic in this field.

a$)$ If $p(x)=x$ and $q(x)=x^2+1,$ what is $p(x)+q(x)$ modulo $P?$

$x+x^{{?}^{{?}^{?}}}2+1$

b$)$ If $p(x)=x^3+x^2$ and $q(x)=x^3+x^2+x+1,$ what is $p(x)+q(x)$ modulo $P?$

$x+1$

c$)$ If $p(x)=x^3+x+1$ and $q(x)=x^3+x^2+1,$ what is $p(x)*q(x)$ modulo $P?$

$x^{{?}^{{?}^{?}}}2+x$

d$)$ If $p(x)=x^3+x^2$ and $q(x)=x^3+x^2+x+1,$ what is $p(x)*q(x)$ modulo $P$

Find D Only