# Introduction to Polynomials

A polynomial is an expression made up by adding and subtracting monomials.
## MonomialsWe start by defining a monomial as a term of the form a x ^{ n}## Examples of Monomials1. 2 x^{ 2}2. - 3 x 3. (1 / 2) x ^{ 7}
## BinomialsWe now define abinomial as a sum of 2 monomials that are not like.
## Examples of Binomials2 x + 8 , - x^{3} + 3 x , (1/2) x^{2} - x
A trinomial as a sum of 3 monomials that are not like.
Examples: 2 x ^{3} + 8 x - 2 , 3 x^{4} - 5 x - 9 , 0.2 x^{2} - x + 4
## PolynomialsApolynomial in x is the sum of any number of monomials and has the following form
a_{n} x^{n} + a_{n-1} x^{n-1} + ... + a_{1} x + a_{0}where the coefficients a_{k} are constant. If coefficient a_{n} is not equal to 0, then n (the highest power) is the degree of the polynomial and a_{n} is the leading coefficient.
## Examples of Polynomials1. -2 x^{3} + 4 x^{2} - 9 x + 12 , leading coefficient -2 and degree 3.
2. ( 1 /3) x ^{5} - x^{3} - 9 x^{2} , leading coefficient 1 / 3 and degree 5.
## Equal PolynomialsTwo polynomials are equal if their corresponding coefficients are all equal.Example: For what values of a, b and c are the polynomials - x ^{2} + 4 x - 9 and a x^{2} + b x^{2} + c
Answer: a = - 1 , b = 4 and c = -9 ## More References and Links to Polynomial FunctionsPolynomial Functions |