Chapter 8.1, Problem 3E

(a)

To determine

The polynomial $f\left(x\right)+g\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.

(b)

To determine

The polynomial $g\left(x\right)+h\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.

(c)

To determine

The polynomial $f\left(x\right)g\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.

(d)

To determine

The polynomial $g\left(x\right)h\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.

(e)

To determine

The polynomial $f\left(x\right)g\left(x\right)+h\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.

(f)

To determine

The polynomial $f\left(x\right)+g\left(x\right)h\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.

(g)

To determine

The polynomial $f\left(x\right)g\left(x\right)+f\left(x\right)h\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.

(h)

To determine

Thepolynomial $f\left(x\right)h\left(x\right)+g\left(x\right)h\left(x\right)$ with all coefficients in ${\mathbb{Z}}_8$.