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October 2, 2023

Polynomials – An integral part of mathematics to comprehend

  • October 21, 2021
  • 4 min read
Polynomials – An integral part of mathematics to comprehend

Polynomials are one of the significant concepts of mathematics that every student studies in their academics. It is one of the crucial concepts, and many of us deal with them across various fields in our real life. Polynomials are classified into various categories based on the degree of a polynomial. Various operations can be performed on polynomials, like addition, subtraction, etc. One such method that is used to perform division on polynomials is synthetic division. In this article, we are going to discuss the degree of polynomial and synthetic division.

Degree of a polynomial

Before discussing the degree of polynomials, let us quickly discuss polynomials. A polynomial is an expression consisting of different algebraic terms. We all have studied linear equations, quadratic equations. They all are an example of a polynomial. One interesting point to note about polynomials is that if we add, subtract or multiply two polynomials. The result we will get will be again a polynomial itself. A polynomial expression contains many elements, few of them are constants and variables. Polynomials are of mainly three types, and they are monomial, binomial, and trinomial. These three are classified based on the number of terms present in them. A monomial consists of only one term, binomial consists of two, and trinomial consists of exactly three terms in the expression. 

As discussed above, a polynomial is an expression consisting of constants and variables. The degree of a polynomial is the highest power of the variable in a polynomial expression. A polynomial degree is easy to find but few points must be taken care of while doing so. We always look for the power of the variables and not of the constant. Suppose the equation given to us is x2+53. In this, the degree of the polynomial is 2 as it is the highest power of the variable. Similarly, always look for the highest power of the variable, if more than one term is there in the equation, like x2+x, in this the degree of the polynomial is 2. A constant is also a polynomial with a degree as zero, as no variable is there. A cubical polynomial consists of the degree of a polynomial as three, quartic has the highest degree as four, and so on. Every student should be able to identify the degree of a polynomial as soon as they look at the expression. 

Synthetic division

We all know about division; synthetic division is just another method of division. It is used when the divisor is a linear factor and we have to perform this operation of division on polynomials. One of the major benefits of using this method for division on a polynomial when compared to the long division method is that in this method, we don’t need to write the variables while performing the polynomial division. Let us take an example, to understand synthetic division in detail.

Let p(x) = 4×2 + 5x – 6 be the polynomial that has to be divided by x + 1. When we want to divide a polynomial P(x) by a linear factor, we write all the coefficients of the expression alone, like in the above example coefficients are 4, 5, and -6. Bring down the first coefficient, multiply it by the divisor, and add the next constant term to it. Perform the same process until we reach the polynomial’s end term. We may easily do complex division using synthetic division and acquire the solutions.

In the above article, we have gone through various crucial aspects of the polynomial. Synthetic division is a great method, and every student should practice it to master it. It helps solve problems quickly in exams. If any student faces any difficulty in solving such maths-related crucial topics, they should take the assistance of Cuemath. It is an online platform that helps students across various countries to master these math topics.