**189-235A:** Basic Algebra I

## Assignment 5

## Due: Wednesday, October 8.

**1**. Page 162, 3.33.

**2-5**. Page 171, 3.34, 3.40, 3.41, 3.43.

**6-7**. Page 178, 3.45, 3.46.

**8.** Let * F* be
a field having infinitely many different elements.

a) If *f* and *g* are two polynomials with coefficients in
*F*, show that
if *f(x)=g(x)* for all *x* in *F*, then
*f=g* (as polynomials).

b) Show that this theorem continues to hold if * F* is
only assumed to be a
domain (having infinitely many elements) and not necessarily a field.

c) Show (by giving an example)
that the conclusion of a) can fail if *F* is a field with finitely many
elements.