Polynomial: Polynomial with variable x, is denoted by p(x) is
expression of the type
are the coeeficients, and x
is variable. is called constant term.
The polynomial has terms.
e.g.
Monomials: A polynomial with one term is
called monomial.
e.g
Binomial: A polynomial with two terms is
called binomial.
e.g.
Trinomial: A polynomial with terms is called trinomial.
e.g.
Constant polynomial: Aconstant polynomial isa
polynomial which is free of variable,and just contains a constant term
e.g.
Degree of
polynomial: It
is the highest power of variable in the expression of polynomial p(x).
The Polynomial has degree .
Cubic polynomial: A polynomial with degree is called cubic polynomial.
e.g.
Quadratic
Polynomial: A
polynomial with degree is called Quadratic polynomial.
e.g.
Linearpolynomial : A polynomial with degree is called Linear polynomial.
e.g. 2x+4
Degree of constant polynomial is zero.
Value of polynomial:
Value obtained after replacing x by a real number k
in the expression of is called value of polynomial at .
For p(x)=
Put x=4
We get p(4) =
.
We say is the value of polynomial at .
Zeroes of
polynomial:The values of x, at which the polynomial p(x) is equal to 0 is
called as zeroes of polynomial.
For e.g.
We get,
So is called zero of the given polynomial.
Remainder theorem:
When polynomial is divided by polynomial , then the remainder will be
p(a).
e.g.
If
Remainder=
Factor theorem:
For polynomial , if , then is factor of
e.g.For
so(x-3) is factor of .
Algebraic
identities:
1)
2)
3)
4)
5)
5)
Or =
6)
Or =
7)
8)
9)