The document discusses polynomials and their properties. It defines what a polynomial is, how they are written in standard form with exponents in descending order, and how to rewrite verbal expressions as algebraic polynomials. Examples are provided of rewriting polynomials in standard form and writing the polynomial expression for the speed of a stone thrown upwards over time. The purpose is to help students understand polynomials and how to frame them from written descriptions.

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

4. Look at the algebraic expressions




153x
10x  x2
2 3 35x  24x  4x
x  x 2

6. 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
2 3
x x x
35  24 
4
3 2
x x x
4  24 
35

7. Can you rewrite all the
polynomials in slide 4 in this
form?
For example :
15+3x can be written as
3x+15

8. Answers
2)
3)
2
x x
 
10
x  x 
x
4) x 
x
2
3 2
4 24 35

9. 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.

10. Solution:
Speed of the stone = 20m/sec
Speed 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

11. 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…

12.  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.

13. For more interesting facts:
http://www.mathsisfun.com
/algebra/
polynomials.html
http://mathonweb.com/hel
p_ebook/html/
poly_0.htm

14. 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 .