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 x
3 + 4 x2 - 9 x + 12 , leading coefficient -2 and degree 3.

2.     ( 1 /3) x
5 - 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

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