Polynomials

ISSUED BY KENDRIYA VIDYALAYA - DOWNLOADED FROM WWW.STUDIESTODAY.COM

Chapter - 2
(Polynomials)
Key Concepts
Constants : A symbol having a fixed numerical value is called a constant.
Example : 7, 3, -2, 3/7, etc. are all constants.
Variables : A symbol which may be assigned different numerical values is known as variable. Example :

C - circumference of circle r - radius of circle

Where 2 &

are constants. while C and r are variable

Algebraic expressions : A combination of constants and variables. Connected by some or all of the operations +, -, X and
Example :

is known as algebraic expression.

etc.

Terms : The several parts of an algebraic expression separated by '+' or '-' operations are called the terms of the expression.
Example :

is an algebraic expression containing 5

terms
Polynomials : An algebraic expression in which the variables involved have only nonnegative integral powers is called a polynomial.
(i)
(ii)

is a polynomial in variable x. is an expression but not a polynomial.

Polynomials are denoted by
Coefficients : In the polynomial

, coefficient of

respectively and we also say that +1 is the constant term in it.
Degree of a polynomial in one variable : In case of a polynomial in one variable the highest power of the variable is called the degree of the polynomial.
Classification of polynomials on the basis of degree.
14

ISSUED BY KENDRIYA VIDYALAYA - DOWNLOADED FROM WWW.STUDIESTODAY.COM

ISSUED BY KENDRIYA VIDYALAYA - DOWNLOADED FROM WWW.STUDIESTODAY.COM

degree

Polynomial

Example

(a)

1

Linear

(b)

2

Quadratic

etc.

(c)

3

Cubic

etc.

(d)

4

Biquadratic

Classification of polynomials on the basis of no. of terms
No. of terms

Polynomial & Examples.

(i)

1

Monomial -

(ii)

2

Binomial -

(iii)

3

Trinomial-

etc. etc. etc.

Constant polynomial : A polynomial containing one term only, consisting a constant term is called a constant polynomial the degree of non-zero constant polynomial is zero.
Zero polynomial : A polynomial