Fundamentals of Polynomials
Types of Polynomials depending on number of terms
Depending upon the number of terms, polynomials are divided into the following categories:
Monomial
A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A few examples of monomials are:
(i) 5x (ii) 3
Binomial
A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two monomials. A few examples of binomials are:
(i) – 5x+3 (ii) 6a4 + 17x
Trinomial
A trinomial is an expression which is composed of exactly three terms. A few examples of trinomial expressions are:
(i) – 8a4+2x+7 (ii) 4x2 + 9x + 7
Multinomials
Expressions with two (or) more terms are called multinomials.
Ex:- \(a \pm b,\,\,2x \pm 3y \pm z\)
Polynomial containing 4 terms (Quadronomial)
Polynomial containing 5 terms (pentanomial ) and so on …
Rules for an Expression to be a Polynomial
An algebraic expression should not consist of –
1. Square root of variables.
2. Fractional powers on the variables.
3. Negative powers on the variables.
4. Variables in the denominators of any fractions.
5. Not a Polynomial example.
6x-2 is not a polynomial since there is negative power on the variable.