A polynomial is a mathematical expression that uses numbers and variable terms. A term of a polynomial is either a constant or the product of a non-zero constant and one or more variables raised to integral powers and following the rules of algebraic manipulation (i.e., addition, subtraction, multiplication, division, raising to an integral power). The constants appearing with each term are called it’s coefficient. The polynomial can be written so as to display all of its terms and their respective coefficients explicitly.
The term “polynomial” refers to a sort of expression. We need to understand expressions before we can talk about polynomials. What is the definition of an expression? A mathematical statement without the equal-to symbol is called an expression. Returning to polynomials, the concept might be stated as follows: “A polynomial is a form of equation in which the exponents of all variables must be a whole integer.”
Like Terms and Unlike Terms
In polynomials, like terms are ones that have the same variable and power. Terms with diverse variables and powers are referred to as unlike terms. As a result, if a polynomial comprises two variables, all powers of the same variable are known as similar terms. Let’s look at some instances to assist us grasp this concept. 2x and 3x, for example, are similar terms. 3y3 and 2x3, on the other hand, are unlike terms.
A polynomial’s degree:
Like terms have the same variable and power in polynomials. Term having a wide range of variables and powers is known as an unlike term. As a result, all powers of the same variable are known as comparable terms when a polynomial has two variables. Let’s have a look at a few examples to help us understand these concepts.
Polynomials in Standard Form
A polynomial in standard form is a polynomial written in the descending power of the variable. Let’s use an example to better comprehend this notion. Take the polynomial 5+2x+x2 and express it in standard form. To present the above polynomial in standard form, we must first determine its degree. The maximum degree of polynomial is 2. Then we’ll see whether there’s a term with a degree less than 2, i.e. 1, and if there’s a word with a degree of zero, which is the constant term.
There are three different types of polynomials.
Polynomials are classified according to their degree and power. There are three basic forms of polynomials, which are given below, based on the number of terms:
Important Polynomial Notes
- Only the ‘+’ or ‘-‘ sign can be used to separate terms in a polynomial.
- The variable’s power must be a whole number for any equation to become a polynomial.
- A polynomial’s addition and subtraction are only feasible between similar terms.
- Constant polynomials refer to all of the numbers in the universe.
Polynomials are used in many ways. Most importantly, they can be employed to describe patterns and relationships between quantities. A lot of polynomial functions involve all three forms because this allows them to model different types of data sets. They also happen to supply mathematicians with a way to define all sorts of real-world phenomena that recur across mathematics, science, and engineering. Some examples include modeling the motion along an axis (e.g., motion diagrams), the flow of fluids (e.g., fluid mechanics) or the oscillations about equilibrium (e.g., oscillations).