Examples of Dividing Polynomials Using Long Division
Example: Divide x2 + 2x + 3 by x – 2.
Solution:
Step 1: Arrenge both Divisors and Dividends in the decreasing order of degree
Dividend = x2 + 2x + 3
Divisor = x – 2Step 2: We will write the dividend and divisor in the long division form, like this:
Step 3: Divide the first term of the dividend by the first term of the divisor, to get the first term of divisor i.e.,
x2/x = x
This means that the first term of the quotient is x.
Step 4: Multiply the divisor (x – 2) by the first term of the quotient (x), and arrenge them under the divident with like terms aligned.
Step 5: Subtracted the result of step 3 from the dividend to get a new polynomial,
Step 6: We will repeat steps 3 and 4 using the new polynomial 4x + 3:
4x/x = 4
Multiplying divisor (x – 2) by the 4,
Step 7: Since the degree of the new polynomial 11, has a degree 0 which is less than the degree of the divisor (x – 2) i.e., 1, we can stop here.
So, the result of dividing the polynomial x2 + 2x + 3 by x – 2 is:
Quotient: x + 4 and Remainder: 11.
Example: Divide x3 + 2x2 – 5x + 1 by x – 2.
Solution:
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