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Free Homework Math Help: Polynomials

 

Polynomials

When two numbers are multiplied, the numbers are called factors. The same is true of variables. Also, when one or more variables are multiplied, the product is called a term. The same is true when the exponent of the variables is a number other than one. Examples of terms are: x, xy, x2y, 4x4y2z3.

A term by itself is also called a monomial. A finite sum of terms is called a polynomial. The terms of a polynomial are separated by the degree of the exponent of the same variables as well as the different variables. Examples of polynomials are: x2+x, 2x3+4x+3, etc. Polynomials are arrainged so that the terms with the largest exponents are to the left while those with the smallest or no exponents are to the right. The largest exponent of the polynomial is also itys degree.

The general form of a polynomial is as follows:

           anxn+an-1x(n-1)+...+a2x2+a1x+a0

where
an, an-1, ..., a2, a1, a0 are real numbers.
Also,
n is a nonnegative integer if an ≠ 0 then n is the degree of the polynomial. The coefficient an is the leading coefficient and a0 is the constant.

A polynomial with one term is a monomial. A polynomial with two terms is a binomial and a polynomial with three terms is a trinomial. Also, a polynomial of degree 2 is called a quadratic function. It can be a monomial, binomial or trinomial. Examples are:

Monomial      x2
Binomial      x2+1
Trinomial      2x2+3x+3

Some of the conditions a function must have to be a polynomial are:

  1. The exponents must be whole numbers.
  2. There cannot be negative or fractional exponents.
  3. The demonimator of a fraction can't have a variable.
  4. The variables can't be under a radical.

It is also important to know how to perform simple operations on polynomials such as addition, subtraction, multiplication and division.


Quadratic Equations
Cubic and Higher Degree Polynomials
Polynomial Division