What Are Polynomials? How do you define the Degree of a Polynomial?
What are Polynomials in Maths: For upon |An algebraic expression that consists of variables and coefficients is called a polynomial. These polynomials involve arithmetic operations such as addition, multiplication, subtraction, and positive integer exponentiation of variables. For example, x2 – 7x + 12 is a polynomial where x is the variable. 1, -7, and 12 are the coefficients, and we use basic arithmetic operations to complete the mathematical expressions. In this article, we will learn more about polynomials and the various aspects associated with this topic. What are Polynomials in Maths?
History of Polynomials
One of the oldest problems existing in Mathematics was how to determine the roots of a polynomial or how to solve algebraic equations. Before the 15th century, equations were written in words. Our journey of discovering algebra starts in Egypt and Babylon. People tried to solve linear, quadratic, and indeterminate equations. Later the Alexandrian mathematicians took these ideas and expanded upon them. This knowledge became a staple in the Islamic world. In the 9th century, the Arab mathematician al-Kwharizmi wrote one of the first books on algebra that consisted of several examples and proofs of theories that we know today. Many other prominent mathematicians such as Euclid, Brahmagupta, Leonardo Fibonacci, Rene Descartes, etc., contributed to a more refined method of solving polynomials that is used in today’s world. What are Polynomials in Maths?
Degree of a Polynomial
The degree of a polynomial is the highest exponent that occurs in the polynomial. It can also be defined as the highest degree of a monomial within a polynomial. Let us see a few examples to get a better understanding of the degree of a polynomial and categorize some basic algebraic expressions. What are Polynomials in Maths?
- Zero Polynomial
Degree = 0
E.g. 9
- Linear Polynomial
Degree = 1
6y – 9
- Quadratic Polynomial
Degree = 2
y2 – 5y + 6
- Cubic Polynomial
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Degree = 3
y3 – y2 – y + 1
As you can see, the highest exponent of a polynomial with one unknown variable becomes the degree of that polynomial. What are Polynomials in Maths?
Classification of Polynomials
There are three types of polynomials
- Monomial
A type of polynomial that consists of only one term in the algebraic expression is known as a monomial. The single term contained in the expression should be a non-zero term. For example, 5y, 7, and 20y7 are all examples of monomials. What are Polynomials in Maths?
- Binomial
A type of polynomial that consists of 2 terms in the expressions is called a binomial. In other words, a binomial can be considered to be a combination of two monomials that are joined together by addition or subtraction operators. What are Polynomials in Maths? For example, 8y + 6, yz5 – zy8
- Trinomial
Such a type of polynomial consists of exactly three terms. For example, y2 – 9y + 9.
How to Study Polynomials?
The first step in learning polynomials is always to generate interest. You can do this by studying the history or fun facts associated with the topic. You can also use math puzzles, worksheets, and fun games to supplement the knowledge you gain from the prescribed textbook. This enables you to not only build a solid foundational understanding of the subject but will also help you to develop several auxiliary skills such as logic, reasoning, and analytical abilities. Additionally, it would help if you practiced different types of questions so that you can improve your speed and accuracy while doing calculations. What are Polynomials in Maths?
Conclusion
As algebra and polynomials are very important mathematical topics, hence a child needs to study them in a well-organized way. Cuemath is a fantastic online educational platform that focuses on clearing a child’s concepts from the roots. The certified tutors use many resources and aim to combine fun with learning to give a kid the best quality of education possible. What are Polynomials in Maths?
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