What is Polynomial?
A polynomial is an expression made up of two or more algebraic terms. They are often made up of different exponents or variables. There are a few amazing facts too about Polynomials like If you add or subtract any polynomial, you will get another polynomial equation. Polynomial equations are usually taken as function and if you graph the equation, there will be a smooth curve without any holes. Here, are some rules about what cannot be a Polynomial?
- Polynomials don’t contain division by variables
- There are no negative exponents in Polynomial.
- Fractional exponents are not available on Polynomial.
- Radical are not considered in Polynomial.
Polynomials are usually divided on the basis of terms and degree. A polynomial with one term is named as monomials, for two terms it will be called as binomials, and for three terms it is taken as Trinomials and so on. Similar is the case for degrees where polynomial with degree two is named as quadratic and for degree three, it is named as cubic. Polynomials may contain the infinite number of terms, so instead of naming them independently, the best idea is to call them polynomials only.
List of Basic Polynomial Formulas
There is a complete list of basic Algebraic formulas that are used when you solve any Polynomial equation. These formulas make your calculation simpler and more interesting to calculate any variable that is unknown yet.
The general Polynomial Formula is written as,
If n is a natural number, an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
(a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
Polynomial Equation & Problems with Solution
A polynomial equation is an expression containing two or more Algebraic terms. Taken an example here – 5x2y2 + 7y2 + 9
This is a polynomial equation of three terms whose degree needs to calculate. Take the first term 5x2y2 – the degree of x is 2 and the degree of y is also 2. So, the degree of the term would be 4. In the next term, 7y2, the degree of y is 2 and the total degree of the term would be two. The third term is a constant. The highest degree of the term would be taken as the degree of Polynomial. SO, the degree of this Polynomial equation is 4.
Question 1: What are the factors of the equation x2 – 4x + 4?
Solution:
= x2 – 2(2x) + 22
= x2 – 2(2)(x) + 22
= (x – 2)2
Question 2: What are the factors of the equation x2 + 7x + 10 ?
Solution:
= x2 + 5x + 2x + 10
= x2 + 5x + 2x + (5)(2)
= (x + 5)(x + 2)
Polynomial Functions
A polynomial function is defined by evaluating a Polynomial equation and it is written in the form as given below –
Why Polynomial Formula Needs?
Polynomial equations are used almost everywhere in a variety of areas of science and mathematics. They are used for Elementary Algebra and to design complex problems in science. The other area of application for Polynomials includes chemistry, physics, economics, social science, calculus, and various types of numeric analysis too.
If we talk about the advanced mathematics then polynomials are used to construct various concept in algebra and geometry. This wide area of application makes Polynomial suitable for high-level concepts in engineering and they are needed to derive multiple formulas or equations in science. The clear understanding of Polynomials concepts can give you a hike in your career especially when you are a scientist or research engineer.