Polynomials are some of the most advanced and significant topics which we study in mathematics. Polynomial is a topic which is taught to children from their primary school days till their higher classes. This branch of mathematics deals with numbers. The concept of finding out the degree of the polynomial provides us the maximum number of solutions that a function could have and the number of times a function will cut the x-axis when represented graphically.
This article deals with polynomial, degree of polynomial and synthetic division.
The degree of the polynomial can be found out by taking the value which has the highest exponential power in a given Equation.
Listed below are some of the applications of the degree of the polynomial.
- The degree of the polynomial is used to find out the maximum number of solutions that a function could have.
- To determine the maximum number of times a function will cut the x-axis when plotted graphically.
- To check whether the polynomial expression is homogeneous, it is necessary to find out the degree of every term. When the degrees of the term are equal, then the polynomial expression can be termed as homogeneous one and when the degrees are not equal, then the expression is called to be non-homogeneous.
These were some of the applications of the degree of the polynomial.
Now, let’s discuss some tips and tricks to easily find out the degree of a polynomial.
- One needs to find out every term of a polynomial.
- Then one needs to collect and combine all the like terms and unlike terms leaving the constant term aside.
- Then one needs to arrange those terms in decreasing order of their powers.
- Then one needs to look at the term which has the highest exponent and that will determine the degree of the polynomial.
- To find out the degree of a polynomial that consists of one variable one needs to look for the largest exponent of the variable in the polynomial.
- To find out the degree of a polynomial with more than one variable, one needs to determine each term of that polynomial, so to take out the degree of each term one can add the exponents.
These were some of the tips and tricks to be kept in mind while taking out the degree of a polynomial.
Now let’s discuss synthetic division.
Synthetic division is a way to divide a polynomial with a linearly varying binomial by only taking the values of the coefficients. In this method of division, we first need to write the polynomials in the simple standard form from the highest degree term to the lowest degree terms. While writing in decreasing powers, one needs to use 0’s as the coefficients for the terms which are missing.
Let’s discuss the steps for carrying out the synthetic division.
- One needs to look at whether the given polynomial is in the standard form.
- After having a check for the standard form, one needs to write the coefficients which are present at the dividend’s place.
- Then, one needs to write the zero of the linear factors which is at the divisor’s place.
- Then, one just needs to bring the first coefficient down.
- After bringing the first coefficient down, He needs to Multiply it with the divisor and then write it below the next coefficient.
- Now, he needs to simply add and write the value below.
- Then, he needs to repeat the previous 2 steps until he gets the last term.
- After getting the last term, one needs to separate the last term which is obtained from the remainder.
- Now he needs to just group the coefficients with the variables to get the value of the quotient.
These are some of the steps to perform synthetic division.
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