In mathematics, a polynomial is an expression of 
  finite length
  constructed from variables and constants, using 
  only the operations
  of addition, subtraction, multiplication, and non-
  negative, whole-
  number exponents. Polynomials appear in a wide 
  variety of areas of
  mathematics and science. For example, they are 
  used to form
  polynomial equations, which encode a wide range 
  of problems, from
  elementary word problems to complicated 
  problems in the sciences;
  they are used to define polynomial functions, which 
  appear in
  settings ranging from basic chemistry and physics 
  to economics and
  social science; they are used in calculus and 
  numerical analysis to
  approximate other functions.
                         Let x be a variable n, be a positive
                         integer and as, a ,a ,….a be constants
                                                   1 2          n
                         (real nos.)
                         Then, f(x) = a xn+ a xn-1+….+a x+x
                                                n        n-1               1      o
                                                a xn,a xn-1,….a x and a are known as
                                                    n      n-1             1            o
                                               the terms of the polynomial.
                                                a ,a ,a ,….a and a are their
                                                     n n-1 n-2            1         o
                                                     coefficient
                                                     s.
                            For example:
                            • p(x) = 3x – 2 is a polynomial in variable x.
                            • q(x) = 3y2 – 2y + 4 is a polynomial in variable y.
                            • f(u) = 1/2u3 – 3u2 + 2u – 4 is a polynomial in variable u.
 •A polynomial of degree 1 is called a Linear
 Polynomial. Its general form is ax+b where a is not
 equal to 0
 •A polynomial of degree 2 is called a Quadratic
 Polynomial. Its general form is ax3+bx2+cx, where a
 is not equal to zero
 •A polynomial of degree 3 is called a Cubic
 Polynomial. Its general form is ax3+bx2+cx+d,
 where a is not equal to zero.
  •A polynomial of degree zero is called a Constant
  Polynomial
                   LINEAR POLYNOMIAL
                          For example:
                  p(x) = 4x – 3, q(x) = 3y are linear
                          polynomials.
                    Any linear polynomial is in the form
                    ax + b, where a, b are real
                         nos. and a ≠ 0.
                   QUADRATIC POLYNOMIAL
                              For example:
                            2               2 
                     f(x) = √3x – 4/3x + ½, q(w) = 2/3w + 4
                     are quadratic polynomials with real
                     coefficients.