# Introduction to Polynomials

 We start by defining a monomial as a term of the form a x n where x is a variable, a is a constant and n is a nonnegative integer. Examples: These are monomials. 1.     2 x 2 2.     - 3 x 3.     (1 / 2) x 7 We now define a binomial as a sum of 2 monomials and a trinomial as a sum of 3 monomials. A polynomial in x is the sum of any number of monomials and has the following form an xn + an-1 xn-1 + ... + a1 x + a0 where the coefficients ak are constant. If coefficient an is not equal to 0, then n (the highest power) is the degree of the polynomial and an is the leading coefficient. Examples: These are polynomials. 1.     -2 x3 + 4 x2 - 9 x + 12 , leading coefficient -2 and degree 3. 2.     ( 1 /3) x5 - x3 - 9 x2 , leading coefficient 1 / 3 and degree 5. Two polynomials are equal if their corresponding coefficients are all equal. Example: For what values of a, b and c are the polynomials - x2 + 4 x - 9 and a x2 + b x2 + c Answer: a = - 1 , b = 4 and c = -9 More references and links to polynomial functions. Polynomial Functions