How to Find the Degree of a Polynomial?
Mar 01, 2021
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Introduction:
In mathematics, polynomials hold great significance and are an integral part of the language of mathematics and algebra. It is widely applied in almost every field of mathematics to represent numbers as a result of various mathematical operations. Many mathematical processes performed in our everyday lives are interpreted as polynomials. They are useful to calculate the price of things in a grocery bill to computing the distance traveled by a vehicle or object can be interpreted as a polynomial. Measuring the perimeter, area, and volume of various geometric shapes can be represented as polynomials. These are just some of the many applications of polynomials.
What is a Polynomial?
Polynomials are the basic building blocks in almost every type of mathematical expression, such as rational expressions. The meaning of the word polynomial is many terms. It refers to a variety of expressions that include constants, variables, and exponents. It is an algebraic expression consisting of variables and exponents that includes the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² - 2x + 5.
For example, x - 7 is a polynomial; so is 66.
How to Find the Degree of a Polynomial?
The degree of polynomial is the highest power of an algebraic expression.
To find the degree of a polynomial, all you have to do is to find the largest exponent in the polynomial. If you want to find the degree of a polynomial in a variety of situations, just follow these steps:
Degree of a Polynomial with one Variable:
Finding the degree of a polynomial with one variable requires arranging the exponents in decreasing order, with the highest value in the first place and the lowest value at last. For example, in this expression -x^5 + x^4 + x, the first term has power 5. The power of a polynomial is only the number in the exponent. Since you've arranged the polynomial to put the largest exponent first, that will help you to find you will find the largest term, which is the degree of this polynomial.
Degree of a Constant Polynomial:
The degree of a constant is zero. If the polynomial contains only a constant value such as 33 or 56, then the degree of this type of polynomial is zero. You can also consider this polynomial as the constant term attached to a variable with the power of 0, which is 1. For example, consider the polynomial 12; you can think of it as 15x^0, 12 x 1, or 12; Which implies that the degree of a constant polynomial is 0.
Degree of a Polynomial with Multiple Variables
Finding a polynomial degree with multiple variables is quite trickier than finding the degree of a polynomial with constants and one variable. To find the degree of a polynomial with multiple degrees, simply add the powers of the variables in each term; it is not required that they are the same variables. The degree of a variable without any degree, such as x or y, is just one.
Let's take the example of the following expression:
5x^4 y^3 z + 4x y^2 + 3x^3 y z^2, In this case, the first term has x^4, y^3, and z^1, which implies 4+3+1= 8, In the second term, x^1 and y^2 that is 1+2 = 3. The third term is 3x^3 y z^2, that is, x^3, y^1, and z^2, i.e., 3+1+2 = 6. Therefore, the degree of the polynomial is 8.
Conclusion:
Learning the concept of polynomials is important as they form the fundamental knowledge for various other maths topics. Cuemath offers interactive learning resources for kids to understand the concept of monomials and polynomials with ease.