Tuesday, 25 October 2011

How to deal with Polynomials

In mathematics general equations are in the form of any polynomial equation which includes multiple terms in it. Polynomial expressions are formed with constants and variables with product of integer coefficient or without integer coefficient. These variables and constants are related to each other by arithmetic operators to form the polynomial equation. Any polynomial equation consists of finite number of derivatives. The standard representation of polynomial equation is in the form of following mathematical expression:

pnxn+.....+ p2x2+ p1x1+ p0x0,

here 'n' is a finite number which tells the highest no. of derivatives in any polynomial equation and ( pn, pn-1, ….... p0) are integer coefficients. Polynomial equation's derivatives may have various order of degree. If all the derivatives are of same order than that expression is said to be as linear polynomial equations otherwise non-linear polynomial equations.

Let us take an example of polynomial equations to explore it more

x2+ 5x + 3 = 4 -------> (1)

y =2 ---------> (2)

x3+ y3=1 -------> (3)

Every polynomial equation is said to be of n- order polynomial equation and the value of 'n' is the highest degree among all the derivatives in the equation.

So in the above examples, the equation first is said to be as 2 – order non -linear polynomial equation because it has highest degree as 2 in all its derivatives and all the derivatives are not of same order that's why it is in non -linear form.

Polynomial functions are also called as monomials, binomials and trinomials depending upon the number of unknown variables in the polynomial function.

If the polynomial function consist derivatives of a single unknown variable than it is said to be a monomial and if derivatives includes two unknown variables than it will be a binomial and so on trimonial on presence of 3 unknown variables.

In the above examples equation (1) and (3) are binomials and (2) is of monomial form

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