Understand the concept of polynomials. Enhance the skill to apply the four fundamental operations involving polynomials. Verbal statements are transacted into algebraic sentences.

INTRODUCTION

We have already acquainted with many usages of algebra in the previous classes. We know how to generalize the mathematical principles based on mathematical operations into algebraic method. We must learn how to classify the algebraic equation based on their peculiarities. Here we are discussing the polynomials, a special category in the algebraic equation.

Look at the algebraic expressions

210 xx x315

32 42435 xxx xx 2

What do we see in all these algebraic expressions?Various positive integral powers of x are multiplied by specific numbers(it may be 1 also), the products are added or subtracted and finally a specific number is added or subtracted (it may be 0).Such algebraic expressions are called polynomials.

A polynomial is usually written with the exponents of x in descending order, the number without x at the end.

For example, is usually written as

xxx

xxx

35244

4243523

32

Can you rewrite all the polynomials in slide 4 in this form?For example :

15+3x can be written as 3x+15

Answers

2)

3)

4) xx

xxx

xx

2

23

2

35244

10

A stone thrown upwards with a speed of 20 meters per second. Find an algebraic expressions which gives the speed of the stone at various times.

Solution:

Speed of the stone = 20m/secSpeed of the stone losses at the rate of 9.8 m/sec.If the lose of speed in one second is denoted by ‘x’ , the speed of stone at various times

=20-9.8x

The knowledge about polynomials is very important in the study of all the areas of mathematics. The main aim of this presentation is to enable the students to understand the idea of a polynomial, to frame a polynomial with the verbal statements given. Hope you have realized the objectives set for the lesson…

Algebraic expressions consisting of just one term is called a monomial. A sum of exactly two monomials is called a binomial. A sum of exactly three monomials is called trinomial. An algebraic expression in which the variables involved have only non-negative integral powers, is called a polynomial. A polynomial is usually written with the exponents of x in descending order, the number without x at the end.

For more interesting facts:

http://www.mathsisfun.com/algebra/polynomials.html

http://mathonweb.com/help_ebook/html/poly_0.htm

REVIEW.• Rewrite the polynomials :

a. 28+2x (2x+28)b. 40+14x+x² (x² +14x+40)c. 20-9.8x (-9.8x+20)

• Find algebraic expressions which give the perimeter and areas of all rectangles with length 1 cm more than the breadth.

(x²+x sq. cm)Note: Hints are given in brackets .