A polynomial is a mathematical expression. Before we go into polynomials, we should first learn about expressions. What exactly is an expression? An expression is defined as a mathematical statement that does not contain the equal-to symbol (=). The definition of polynomials is as such: “A polynomial is a form of equation in which the exponents of all variables must be whole numbers.” The degree of polynomial is the greatest sum of its exponents. Consider the following example. The degree of a polynomial 5x4 + 8 is four. What is the degree of the polynomial if more than one variable is present?
Let’s look at 3xy to see what I mean. The power of each variable x and y in the preceding polynomial is 1. Add the powers of all the variables in a phrase to compute the degree of a polynomial with more than one variable. As a result, the degree of the given polynomial (3xy) is 2.
What Are Polynomials?
Polynomials are an essential component of algebra. Polynomials are made up of two words: Poly (many) and Nominal (terms). It is classified as monomial, binomial, or trinomial based on the number of words included in the phrase. We can join polynomials using arithmetic operations like addition, subtraction, multiplication, and division, but they are not divisible by a variable.
To understand the topic in a fun and interesting way, you can visit the Cuemath website.
How do you recall the different sorts of polynomials? Consider the concept of cycles!
There are three types of bicycles: monocycles (one wheel), bicycles (two wheels), and tricycles (three wheels). Let’s go through the types of Polynomials –
- Monomial- A monomial is a form of polynomial expression that comprises just one term, which must be non-zero.
- Binomial – A Binomial equation has only two terms. It can be constructed by adding or subtracting the sum or difference of two or more monomials.
- Trinomial – A trinomial phrase is made up of exactly three terms.
Like & Unlike Terms in Polynomials
In polynomials, like terms are defined as the ones that have the same variable and power. Unlike words are those that have distinct variables and different powers. As a result, if a polynomial comprises two variables, all the equal powers of any ONE variable are referred to as similar terms.
Arithmetic Operations on Polynomials
Basic mathematical operations may be performed on polynomials in the same way that they can be performed on integers. When polynomials are added, subtracted, multiplied, or multiplied by another polynomial, the result is another polynomial, and when polynomials are divided, the result is a rational expression. The following are the basic operations on polynomials:
- Polynomial addition – The addition of polynomials is similar to the addition of integers; the only difference is that we must pair together like terms, that is, terms of the same variable and power, and then add them up. The addition of polynomials is one of the fundamental operations used to raise or reduce the value of polynomials. The core rules are the same whether you want to add integers or polynomials.
- Polynomial subtraction – Subtraction of polynomials is analogous to subtraction of two integers. Only the like terms of the polynomial must be aligned and then subtracted.
- Polynomial multiplication – Using the principles of exponents, polynomial multiplication follows the commutative property, distributive property, associative property, and so on.
- Polynomial division – The division of polynomials is the process of dividing a given polynomial by another polynomial that has a lower degree than the dividend.
What Makes Polynomials Unique?
- The polynomial’s Resulting Degree is always the same after the addition and subtraction of polynomials.
- The multiplication of polynomials yields a higher degree of polynomial.
- The polynomial division may or may not produce a polynomial.