An expression of the form 
where 
, 
, 
are real numbers and 
is called a polynomial in 
.
Degree of a polynomial: The highest power of the variable in a polynomial is called degree of the polynomial.
Zero polynomial: The polynomial “0”, which has no term at all, is called Zero polynomial.
Constant Polynomial: It is a polynomial of degree 0. The value of constant function is constant irrespective of values of “x”.
Linear polynomial: A polynomial of degree one is called a first-degree or linear polynomial. The general form of such a polynomial is 
, where 
. In a linear polynomial the maximum number of terms is two.
Quadratic polynomial: A polynomial of degree two is called a second degree or quadratic polynomial. Its general form is
, where 
. In a Quadratic polynomial the maximum number of terms is three.
Cubic polynomial: A polynomial of degree three is called a third-degree or cubic polynomial and is represented as 
, where
.
Such a polynomial can have a maximum of four terms.
Zeros of a Polynomial: Roots of a polynomial: It is a solution to the polynomial equation p(x)=0 i.e. a number “a” is said to be a zero of a polynomial if p(a) = 0.
If we draw the graph of p(x) =0, the values where the curve cuts the X-axis are called Zeros of the polynomial.
Methods to Determine Zero of a Polynomial
Trial and error Method:
Equating polynomial to zero: In this method, you can find the zero of the polynomial by taking 
as the subject.
, 
, 
,
p(a) = 0
Remainder= Dividend – (Divisor × Quotient)
Remainder Theorem: if 
is a polynomial in 
, and 
is divided by 
then the remainder is 
i.e, 
. Here 
Based on the remainder theorem:
If a polynomial 
is divided by
, then the remainder is
.
If a polynomial 
is divided by
, then the remainder is 
.
If a polynomial 
is divided by
, then the remainder is 
.
Remainder= Dividend – (Divisor × Quotient)
p(a) or 
or 
or 
A 
is an 
consisting of multiple terms of 
These terms are combined by using mathematical operators – addition, subtraction and multiplication.
The 
of the 
must be
.
The 
of the 
in a 
is called 
A term can be a 
, a 
or a product of the two.
A real number that precedes the variable is called the 
.
The general form of a 
is 
where 
, …. 
, 
are real numbers and 
is called a polynomial in 
of degree n
A polynomial whose degree is equal to two is called a Quadratic Polynomial.
A polynomial whose degree is equal to three is called a cubic Polynomial.
Factor Theorem:
is a polynomial and 
is a real number, if 
is divided by a linear polynomial
, then the remainder is
.
We know that the algebraic identities of second degree are
These identities can be used to factorise quadratic polynomials.
A polynomial is said to be cubic polynomial if its degree is three
The algebraic identities used in factorising a third degree polynomial are:
Cubic polynomials can be factorised using Factor theorem
Factor theorem:
is a polynomial and 
is a real number, if
, then 
is a factor of
Note Blast 