2.1 Simplifying Algebraic Expressions
... Monomial – A polynomial with a single variable term. Example: Part a) in Example 3 is a monomial Binomial – A polynomial with two terms. Example: Part b) in Example 3 is a binomial Trinomial – A polynomial with three terms. Example: Part c) in Example 3 is a trinomial Algebraic Expression vs. Polyno ...
... Monomial – A polynomial with a single variable term. Example: Part a) in Example 3 is a monomial Binomial – A polynomial with two terms. Example: Part b) in Example 3 is a binomial Trinomial – A polynomial with three terms. Example: Part c) in Example 3 is a trinomial Algebraic Expression vs. Polyno ...
University of Toledo Algebra Ph.D. Qualifying Exam April 21, 2007
... is cyclic of degree |K : F | = n. If d is any divisor of n, show that there is a unique intermediate field L such that L/F is cyclic of degree d. (b) Assume (a special case of) Dedekind’s theorem that, for any natural number n, there are infinitely many primes of the form kn + 1, k ∈ Z. Prove that f ...
... is cyclic of degree |K : F | = n. If d is any divisor of n, show that there is a unique intermediate field L such that L/F is cyclic of degree d. (b) Assume (a special case of) Dedekind’s theorem that, for any natural number n, there are infinitely many primes of the form kn + 1, k ∈ Z. Prove that f ...
