Polynomial Basics
Poly means “many”
and -nomials means “terms”.
We can
define a polynomial as an algebraic expression with many terms written together
using addition, subtraction and multiplication and non negative integer
exponents.
Some examples of polynomials are given below:
- 2
- 2x
- 2xyz
- 3x + 7
- x² - y²
- 4x³ - 4xy – 3x + 2
Basic terminology associated with polynomials:
Variables:
The unknown
quantities which can be known under different conditions and can have
difference values depending upon the conditions.
For example; number of cars in
a mall's parking lot, is a variable as it keeps on changing every moment.
We use
alphabet letters like “x” or “y” to represent variables.
Coefficients: Numbers multiplying to the variables in
a polynomial are called coefficients.
For example; in polynomial 3x + 7 the
coefficient of “x” is 3.
Terms: Terms in a polynomial are separated
by plus or minus signs (keep in mind that we keep the negative sign with each
term).
All the polynomials are made up of terms.
For example;
polynomial 3x - 7 has two terms: “3x” is the first term and “-7”
is the second term.
Degree: Degree of a polynomial is the degree
of term with the highest exponent.
For example; Degree of 4x³ - 4xy – 3x + 2 is 3.
Constant
Term: Term in a
polynomial without a variable is called the constant term.
For example; 4x³ - 4xy – 3x + 2 has 2 as the constant
term.
Monomial:
A polynomial with
only one term is called a monomial. Mono means “one” and mial means “term”.
All
the rational numbers are monomials.
For example; 2 is a monomial. 2x, -4xy and
5xyz are some more examples of monomials.
Binomial:
A polynomial with
two unlike terms is called a binomial. Bi means “two” and mial means “term”.
For example; 3x – 5 is a binomial. x² - y² is another example of a binomial.
Trinomial:
A polynomial with
three unlike terms is called a trinomial.
For example; 2x – 3y + 7 is a
trinomial.
