Dividing Polynomials
What is a Polynomial?
A polynomial is a mathematical expression that contains one or more terms involving variables raised to powers and coefficients. General polynomial of degree n is given by:
anxn + an−1xn−1 + … + a2x2 + a1x + a0
Where a0, a1, a2, . . ., an are the real coefficients.
What is Polynomial Division?
Polynomial division is a process of dividing a polynomial by another polynomial.
What is the Degree of a Polynomial?
The degree of a polynomial is the highest power of the variable in the polynomial.
What is Long Division of Polynomials?
Long division of polynomials is a method of dividing a polynomial by another polynomial,which is similar to long division of numbers.
What is Synthetic Division of Polynomials?
Synthetic division of polynomials is a shorthand method of polynomial division used when dividing a polynomial by a linear polynomial of the form (x – a), where a is a real constant.
What is Remainder Theorem?
In simple words, remainder theorem states that if a polynomial f(x) is divided by x – a, the remainder is equal to f(a).
What is Factor Theorem?
In simple words, factor theorem states that for a polynomial f(x) if f(a) = 0, then (x – a) is a factor of f(x).
How to know if One Polynomial is Divisible by Another?
One polynomial is divisible by another if the degree of the first polynomial is greater than or equal to the degree of the second polynomial, and if the second polynomial is a factor of the first polynomial.
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