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Polyomials

POLYNOMIALS IN ONE VARIABLE

Let us begin by recalling that a variable is denoted by a symbol that can take any real value.

We use the letters, x,y,z etc. To denote variables. We have algebraic expressions

2x,3x,-x,3x/4.... all in one variable x. These expressions are of the form (a constant)*(some power of variable). Now, suppose we want to find the perimeter of a square we use the formula   p=4s.

Here ‘4’ is a constant and ‘s’ is a variable, representing the side of a square. The side could vary for different squares.

Observe the following table:

 Side of square (s) Perimeter (4s) 4 cm 5cm 10cm P=4 * 4 = 16 cm P=4 * 3 = 20 cm P=4 * 10 = 40 cm

Here the value of the constant, i.e. ‘4’ remains the same throughout this situation. that is the value of the constant does not change in a given problem, but the value of the variable (s) keeps changing.

Suppose we want to write an expression which is of the form ‘(a constant)*(a variable)’ and we do not know, what the constant is, then we write the constants as a,b,c...etc. So these expressions in general will be ax,by,cz,....etc. here a,b,c... are arbitrary constants. You are also familiar with other algebraic expressions like

X2, x2 +2x+1, x3 +3 x2 -4x+5.

All these expressions are polynomials in one variable.

DEGREE OF THE POLYNOMIAL       