Polynomials are algebraic expressions that may comprise of exponents which are added, subtracted or multiplied. Polynomials are of different types. Namely, Monomial, Binomial, and Trinomial. A monomial is a polynomial with one term. A binomial is a polynomial with two, unlike terms. A trinomial is an algebraic expression with three, unlike terms. In the following section, we will study about polynomials and types of polynomials in detail.
What is a Polynomial?
In simple words, polynomials are expressions comprising a sum of terms, where each term holding a variable or variables is elevated to power and further multiplied by a coefficient. Amusingly, the simplest polynomials hold one variable.
Types of Polynomials
Let us get familiar with the different types of polynomials. It will form the base to further learning.
Monomials – Monomials are the algebraic expressions with one term, hence the name “Mono”mial. In other words, it is an expression that contains any count of like terms. For example, 2x + 5x + 10x is a monomial because when we add the like terms it results in 17x. Furthermore, 4t, 21x2y, 9pq etc are monomials because each of these expressions contains only one term.
Binomials – Binomials are the algebraic expressions with two unlike terms, hence the name “Bi”nomial. For example, 3x + 4×2 is binomial since it contains two unlike terms, that is, 3x and 4×2. Likewise, 10pq + 13p2q is a binomial.
Trinomials – Trinomials are the algebraic expressions with three unlike terms, hence the name “Tri”nomial. For example- 3x + 5×2 – 6×3 is a trinomial. It is due to the presence of three, unlike terms, namely, 3x, 5×2 and 6×3. Likewise, 12pq + 4×2 – 10 is a trinomial.
Polynomial – Types
There is another type of polynomial called the zero polynomial. In this type, the value of every coefficient is zero. For example: 0x2 + 0x – 0
Degree of a Polynomial
It is simply the greatest of the exponents or powers over the various terms present in the algebraic expression.
Example: Find the degree of 7x – 5
In the given example, the first term is 7x, whereas the second term is -5. Now, let us define the exponent for each term. The exponent for the first term 7x is 1 and for the second term -5, it is 0. Since the highest exponent is 1, the degree of 7x – 5 is also 1.