Polynomials in one variable, Mathematics

Polynomials

In this section we will discuss about polynomials.  We will begin with polynomials in one variable.

Polynomials in one variable

Polynomials in one variable are algebraic expressions which contain terms in the form axwhere n refer to a non-negative (that means positive or zero) integer and a refer to a real number and is termed as the coefficient of the term.  The degree of a polynomial in one variable is the biggest exponent in the polynomial.

Note that we will frequently drop the "in one variable" part and only say polynomial. Here are instance of polynomials and their degrees.

5x12 - 2x6 + x5 -198x + 1                                                          degree : 12

x4 - x3 + x2 - x + 1                                                                    degree : 4

56x23                                                                                        degree : 23

5x - 7                                                                                       degree : 1

-8                                                                                              degree : 0

Thus, a polynomial doesn't have to contain all powers of x . Also, polynomials can contain a single term.

Here are some instances that aren't polynomials.

4x6 + 15x-8 +1

5 √ x - x+ x2

2/x +x3 -2 = 2x-1+x3-2

The first one isn't polynomial as it has a negative exponent and all exponents in a polynomial must be positive.

To illustrate why the second one isn't a polynomial rewrite it a little.

                               5 √ x - x+ x2 = 5x1/2-x+x2

By changing the root to exponent form we illustrates that there is rational root in the algebraic expression.  In the algebraic expression all of the exponents have to be integers in order for the algebraic expression to be a polynomial.  As a general rule of thumb if an algebraic expression contain a radical in it then it isn't polynomial.

Let's rewrite the third equation to see why it isn't polynomial.

2/x +x3 -2 = 2x-1+x3-2

Thus, this algebraic expression really contains a negative exponent in it and it isn't allowed.  Another rule of thumb is if there are variables in the denominator of a fraction then the algebraic expression isn't a polynomial.

Another rule of thumb is if there are any variables in denominator of fraction then the algebraic expression isn't a polynomial.

Notice that it doesn't mean that radicals and fractions aren't let in polynomials. They only can't involve the variables. For example, the following is a polynomial

1854_Polynomials in one variable.png

There are many radicals & fractions in this algebraic expression, however the denominators of the fractions are only numbers and the radicands of each radical are only a numbers. In the algebraic expression each x appears into the numerator and the exponent is a positive (or zero) integer. Hence this is a polynomial.

Posted Date: 4/6/2013 2:20:26 AM | Location : United States







Related Discussions:- Polynomials in one variable, Assignment Help, Ask Question on Polynomials in one variable, Get Answer, Expert's Help, Polynomials in one variable Discussions

Write discussion on Polynomials in one variable
Your posts are moderated
Related Questions
my daughter in kg now how can i train her to develop skills in undertanding the basics of all subjects how can i start teaching other than schol

John and Charlie have a whole of 80 dollars. John has x dollars. How much money does Charlie have? This problem translates to the expression 42 + (11 - 9) ÷ 2. Using order of o

FIRST OF ALL I WANNA KNOW THECHNIQUES, I CAT DIVIDE BIG BIG NUMBERS , EVERYTHING IN MATH IIS VERY HARD FOR ME I HOPE YOU CAN HELP ME

Find an integrating factor for the linear differential equation and hence Önd its general solution: SOLVE T^ 2 DY DX+T2

Rule 1 The logarithm of 1 to any base is 0. Proof We know that any number raised to zero equals 1. That is, a 0 = 1, where "a" takes any value. Therefore, the loga

which one of the following examples represents a repeating decimal? 0.123123,1.111114,0.777777,4.252525?

One coin is tossed thrice. what will be the probability of getting neither 3 heads nor 3 tails

evaluate limit as x approaches 0 (x squared times sin (1/x)

1. Build an equation for a hyperboloid of two sheets with the following properties: a. The central axis of the hyperboloid is the y-axis b. The two sheets are 4 units apart, an

larry spends 3/4 hours twice a day walking and playing with his dog. He spends 1/6 hours twice a day feeding his dog. how much time does larry spend on his dog each day?