4.1 Introduction to Polynomials

In this section, we will learn some terminologies about polynomials.  

 

A term is a product of a number and a variable (or variables) with a power (or powers). The number in the term is called the coefficient of that term. For example:

• $2a^5$ is a term, and the coefficient is $2$. 
• $ -3xy^2$ is a term, and the coefficient is $-3$. 
• $2.5u^3v^5w^7$ is a term, and the coefficient is $2.5$.
•  $6$   is a  terms. It is a constant term, and the coefficient is $6$.  

A polynomial is a sum of terms. 

• For example: $x^2+3x+7$, $x^2y+\frac{1}{6}xyz^2-8y^2z^2$ are polynomials. 

A polynomial with one term is called a monomial. 

• For example: $2a^5$, $-3xy^2$ are monomials. 

A polynomial with two terms is called a binomial. 

• For example: $5x^2+3x$, $-3xy^2+2$ are binomials.

A polynomial with three terms is called a trinomial. 

• For example: $3x^2+5x-1$ is a trinomial.

The degree of a polynomial is the highest power of the variable(s) that has a non-zero coefficient. For example:

• The degree of $-2x^3+4x^2-5x+2$ is $3$.
• The degree of $2x+3$ is $1$.
• The degree of a constant monomial $6$ is $0$, because $6=6x^0$.