this overview of polynomials

2. Introduction
Constant :-component which never change its
value or magnitude is known as constant for
example all real no. Are always constant as they
never changes its values.
Variable :-component of any term or expression or
equation which varies situation is known as
variable.
Term :-term is an element which is combination of
4 signs , numbers , variable and power or a term
always has 4 things sign + or-

3. Types of terms
 Like terms – two or more having
same type of variable and same power
on them are said to be like terms for
example 3x ,-7/2x,8/9x , are like terms.
 Unlike terms –terms if they are not
like then they are known as unlike
terms for example 7a , 8b , 19/3c are
unlike terms.

4. What is polynomial ?
An algebraic expression in the form of : 2a2
+3b+5c+6x,…..+…….
Different types of polynomials:-
1.Monomial :-expression have single term.
2.Binomial :- expression have two terms.
3.Trinomial :-expression have three term.
4. Multinoamil :-expression have more than three
terms.
5.Zero polynomial:-number itself is known as
zero polynomial.

5. Degree of a polynomial
1.Linear polynomial :- A polynomial of the form ;ax +
b, a = 0 is known as linear polynomial its degree is
always zero it may be monomial or binomial . It may be
monomial or binomial for example each of polynomial
2x , -3x is a linear polynomial as well as monomial and
linear polynomial.
2. Quadratic polynomial :- an algebraic expression
of type ax2 +bx +c,a is not equal 0 is known as quadraic
polynomial, or we can say that polynomial of degree2 is
known as quadraic polynomial, quadratic polynomial
can be a monomial , binomial or trinomial.

6. 3. cubic polynomials – a polynomial
of the form of ax3+bx2+cx+d , a=0 is
known as cubic polynomial . A cubic
polynomial may be monomial ,
binomial , trinomial , multinomial .

7. VALUE AND ZEROES OF POLYNOMIAL
 Value of a polynomial
The value of a polynomial p(x) at x = a is
p(a) . Obtained on replacing x by a .
 Zeroes of a polynomial
In general we say that (a) is a zero of
polynomial p(x) at a such that p(a)=0 .

8. Important points to remember :
 A constant polynomial does not has any
zero .
 0 may be a zero of a polynomial .
 Every linear polynomial has one and only
one zero .
 A polynomial can have repeated zeroes .
 Number of zeroes of a polynomial cannot
exceed its degree.

9. Important points about Polynomials:
A polynomial can have many terms but not infinite terms.
Exponent of a variable of a polynomial cannot be negative.
This means, a variable with power - 2, -3, -4, etc. is not
allowed. If power of a variable in an algebraic expression is
negative, then that cannot be considered a polynomial.
The exponent of a variable of a polynomial must be a whole
number.
Exponent of a variable of a polynomial cannot be fraction.
This means, a variable with power 1/2, 3/2, etc. is not
allowed. If power of a variable in an algebraic expression is in
fraction, then that cannot be considered a polynomial.
Polynomial with only constant term is called constant
polynomial.
The degree of a non-zero constant polynomial is zero.
Degree of a zero polynomial is not defined.