About This Lesson
We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position, and repeat.
Polynomials are algebraic expressions that consist of variables and coefficients. It is written in the following format: 5x2 + 6x - 17. This polynomial has three terms that are arranged according to their degree. The term with the highest degree is placed first, followed by the lower ones. Dividing polynomials is an algorithm to solve a rational number that represents a polynomial divided by a monomial or another polynomial. The divisor and the dividend are placed exactly the same way as we do for regular division.
Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder. The terms of the polynomial division correspond to the digits (and place values) of the whole number division. This method allows us to divide two polynomials.
How To: Given a polynomial and a binomial, use long division to divide the polynomial by the binomial
- Set up the division problem.
- Determine the first term of the quotient by dividing the leading term of the dividend by the leading term of the divisor.
- Multiply the answer by the divisor and write it below the like terms of the dividend.
- Subtract the bottom binomial from the terms above it.
- Bring down the next term of the dividend.
- Repeat steps 2–5 until reaching the last term of the dividend.
- If the remainder is non-zero, express as a fraction using the divisor as the denominator.
Key Note:
It is important to teach the concept of multiplying and dividing polynomials together in order for the students to understand the full concept of multiplication and division. It is also important emphasis that multiplying and dividing polynomials is similar to multiplying and dividing real numbers.
