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# Subtracting Polynomials

## Division of Polynomials

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Setup the long division as you would do with whole numbers, with the first polynomial called the dividend under the long division line, and the polynomial we are dividing by called the divisor on the left:. Make sure you write the terms left to right from highest degree to lowest degree for both the dividend and the divisor. The long division process goes as follows: Imagine taking just the highest degree term from the dividend in our example, x2 and dividing it by the highest degree term of the divisor in our example, x.

The result is the first term of our "quotient". In our example, the result will be x. Usually, you should write the answer above the term of the same degree as the result:. Write this result below the dividend, making sure you line up each term of the result under the term in the dividend with the same degree:.

One way to do this without losing track of signs is to reverse all the signs of the terms of our result and add like terms:.

Note that the first term will always cancel out and possibly others will as well. Now, we repeat the process of long division, taking the highest degree of our new polynomial which is 2x and dividing it by the highest degree term of the divisor again, x ; the result is 2.

That is our second term of our quotient, and we write it as follows:. We stop once we have no more terms to bring down. The result from the last step is the remainder. To learn more, visit our Earning Credit Page. Not sure what college you want to attend yet? The videos on Study.

Students in online learning conditions performed better than those receiving face-to-face instruction. By creating an account, you agree to Study. Explore over 4, video courses. Find a degree that fits your goals. Start Your Free Trial Today. This homework help resource uses simple and fun videos that are about five minutes long. Algebra II - Polynomials: Test your knowledge with a question chapter practice test.

View all practice tests in this course. How to Evaluate a Polynomial in Function Notation This lesson will review how to evaluate polynomials in function notation.

Understanding Basic Polynomial Graphs This lesson will cover understanding basic polynomial graphs. Basic Transformations of Polynomial Graphs The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs.

How to Add, Subtract and Multiply Polynomials Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. Defining Expressions In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions.

How to Divide Polynomials with Long Division Arithmetic long division and polynomial long division are very similar. Dividing Polynomials with Long and Synthetic Division: Operations with Polynomials in Several Variables In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. Test your knowledge of this chapter with a 30 question practice chapter exam.

Other Practice Exams in this course. Test your knowledge of the entire course with a 50 question practice final exam. Earning College Credit Did you know… We have over college courses that prepare you to earn credit by exam that is accepted by over 1, colleges and universities.

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Browse Browse by subject. Start your FREE trial. What best describes you? We said, " When you subtract integers, you must add the opposite. We also talked about the Keep - Change- Change Rule. That rule applies to polynomials as well. Your first step is to change the subtraction problem to an addition problem.

Then you add, just as you did in the adding polynomials lesson. Once we change this problem to an addition problem, we will use the horizontal method for solving. Did you notice how you first used the Keep - Change - Change rule to change the problem to an addition problem? Once you have the addition problem you just add like terms.

## Main Topics

Subtracting Polynomials is very similar to adding polynomials. In fact, we will be changing the subtraction problem to an addition problem. In the Pre-Algebra section of the website, we started out by reviewing integers.

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Subtracting Polynomials Subtracting is the inverse of addition, so the difference between adding and subtracting polynomials is that each term subtracted has the opposite sign. For example, -(2x 3 + 4x 2 +12x +42) is -2x 3 -4x 2 x and –(2x 2 x – 36) is .