Dividing Polynomial by Binomial
Binomial is a polynomial that consists of two terms. There are two ways we can divide a polynomial by a binomial. If a binomial is the factor of the given polynomial, then we will factorize the polynomial and eliminate the common factor. However this is not the case always, in case there is no common factor between the binomial and the polynomial to be divided then we will using the Long Division Method.
Dividing Polynomial by Binomial using Factorization
Factorization is the method of writing the given polynomial into product of its factors. If the binomial by which we are dividing a given polynomial is the factor of the given polynomial then we can eliminate the binomial and we are left with the other factor as the quotient. This can be better understood by the example given below:
Example: Divide x2 + 4x + 3 by x + 1
Solution:
We have the Polynomial x2 + 4x + 3 as dividend
The binomial x + 1 is our divisior
We will factorize the polynomial x2 + 4x + 3 using Middle Term Splitting method
⇒ x2 + 4x + 3 = x2 + 3x + x + 3 = x2 + 3x + x + 3 = x(x + 3) + 1(x + 3) = (x + 1)(x + 3)
Now we can do the division as follows
(x2 + 4x + 3)/(x + 1) = (x + 1)(x + 3)/(x + 1)
Now we will eliminate the common part (x + 1).
Hence we are left with (x + 3) as the quotient.
Dividing Polynomial by Binomial using Long Division Method
Long Division Method is the conventional method of dividing polynomial when there is no common factor between the given polynomial and the binomial. This can be understood by following example
Example: Divide 2x2 + 7x – 3 by 2x + 1
Solution:
The process of dividing polynomial by a binomial using Long Division Method is explained in the image added below:
Dividing Polynomials – Long Division Algorithm
Dividing Polynomials as the name suggests the process of division of a polynomial by another polynomial. It is also called Polynomial Division. As we know, any expression with one variable with its various powers and coefficients is called a polynomial. The most general form of a polynomial is given as:
anxn + an−1xn−1 + … + a2x2 + a1x + a0
Where a0, a1, a2, . . ., an are the real coefficients. In Dividing Polynomial we divide the polynomial with a higher degree by a polynomial (that can monomial, binomial, trinomial, or any other higher degree polynomial) with less degree.
In this article, we will learn about all the necessary topics for the division of polynomials such as methods of division i.e., Long Division Method, Synthetic Division, etc. Also, we will learn how to solve problems related to Dividing Polynomials.
Table of Content
- What is Dividing Polynomials?
- Long Division of Polynomials
- How to Divide Polynomials Using Long Division
- Examples of Dividing Polynomials Using Long Division
- Synthetic Division of Polynomials
- How to Divide Polynomials Using Synthetic Division
- Examples of Dividing Polynomials Using Synthetic Division
- Dividing Polynomial by Monomial
- Dividing Polynomial Using Splitting the Term Method
- Dividing Polynomial Using Factorization Method
- Examples of Dividing Polynomial by Monomial
- Dividing Polynomial by Binomial
- Dividing Polynomial by Binomial using Factorization
- Dividing Polynomial by Binomial using Long Division Method
- Common Mistakes to Avoid When Dividing Polynomials
- Sample Problems on Dividing Polynomials
- Dividing Polynomials Worksheet