PDF on arxiv.org - at www.arxiv.org.
PDF on arxiv.org - at www.arxiv.org.

5A Objective: Classify, add, and subtract polynomials Multiply a
5A Objective: Classify, add, and subtract polynomials Multiply a

...  Dividing a polynomial by a polynomial (see example below) 1. Arrange terms of dividend and divisor in general form. If term is missing from, add the terms with a coefficient of 0 2. Divide first term of dividend by first term of divisor. This is first term of quotient. 3. Multiply first term of qu ...
ON SQUARE ROOTS OF NORMAL OPERATORS1 768
ON SQUARE ROOTS OF NORMAL OPERATORS1 768

Exercises for the Lecture on Computational Number Theory
Exercises for the Lecture on Computational Number Theory

Distances between the conjugates of an algebraic number
Distances between the conjugates of an algebraic number

The function f(x) = - (x - 3)2 + 4 has a critical point at x = 3
The function f(x) = - (x - 3)2 + 4 has a critical point at x = 3

... A ____________ is caused in the graph of a rational function when the same factored term appears in both the numerator and denominator. ...
Chapter 2 Assignment Sheet Precalculus Honors 16-17
Chapter 2 Assignment Sheet Precalculus Honors 16-17

Intro to Polynomials
Intro to Polynomials

... We can classify polynomials by the number of terms: Monomial: 1 term Think about other words with the prefix mono: ...
Section V.9. Radical Extensions
Section V.9. Radical Extensions

Look at notes for first lectures in other courses
Look at notes for first lectures in other courses

Polynomial
Polynomial

Notes - UCSD Math Department
Notes - UCSD Math Department

Lecture 6 1 Some Properties of Finite Fields
Lecture 6 1 Some Properties of Finite Fields

Algebra 1 ELG HS.A.3: Perform arithmetic operations on polynomials.
Algebra 1 ELG HS.A.3: Perform arithmetic operations on polynomials.

MATH 361: NUMBER THEORY — TENTH LECTURE The subject of
MATH 361: NUMBER THEORY — TENTH LECTURE The subject of

section 2.4: complex numbers
section 2.4: complex numbers

... The real number line (below) exhibits a linear ordering of the real numbers. In other words, if c and d are real numbers, then exactly one of the following must be true: c < d , c > d , or c = d . ...
THE FERMAT EQUATION 1. Fermat`s Last Theorem for n = 4 The proof
THE FERMAT EQUATION 1. Fermat`s Last Theorem for n = 4 The proof

On the Reducibility of Cyclotomic Polynomials over Finite Fields
On the Reducibility of Cyclotomic Polynomials over Finite Fields

Problem Set 3
Problem Set 3

14. The minimal polynomial For an example of a matrix which
14. The minimal polynomial For an example of a matrix which

MATH 260 2001/2002 Midterm Exam 1
MATH 260 2001/2002 Midterm Exam 1

The Intermediate Value Theorem
The Intermediate Value Theorem

Complex exponentials: Euler`s formula
Complex exponentials: Euler`s formula

“Fixing” Removable Discontinuities
“Fixing” Removable Discontinuities

Full text
Full text

Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. The equivalence of the two statements can be proven through the use of successive polynomial division.In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.