How to do Long Division with Polynomials (With easy steps by step guide)

Dividing polynomials can be tricky for many students. Unlike simple arithmetic division, long division with polynomials requires a deep understanding of the basics of algebra.

However, I believe with the right steps and strategies, doing long division with polynomials can be a breeze.

In this post, I will provide you with a step-by-step guide to help you learn how to divide polynomials. Check out this article to explore more about how to easily factor polynomials, including 5 methods.

Step 1: Properly Set Up The Problem

Like any other math problem, the first step in dividing polynomials is to set up the equation. We typically write the equation in the form of (dividend)/(divisor) = (quotient) + (remainder).

For example, if we were to divide x³ + 3x² + 2x + 1 by x + 1, our equation would look like this:

(x³ + 3x² + 2x + 1) / (x + 1) = (quotient) + (remainder)

Step 2: Divide The First Term

The next step is to divide the leading term of the dividend by the leading term of the divisor; in other words, divide the first term of the dividend by the first term of the divisor. In our example:

• We would divide x³ by x, which gives us x².
• We then write this term above the dividend as the first term of the quotient.
• Multiply the divisor by this term and subtract the result from the dividend.

Step 3: Bring Down the Next Term

After we subtract the result of the multiplication, we bring down the next term of the dividend and place it next to the remainder from the previous step.

In our example, we would bring down 3x² and place it next to the -x² remainder to form 2x².

Step 4: Repeat the Process

We then repeat the same process of dividing the first term of the 2x² by the first term of the divisor, which is x, which gives us 2x, which we write above the dividend.

We then multiply this term by the divisor and subtract the result from the remaining dividend. We bring down the last term of the dividend, 2x + 1, and repeat the process until there are no more terms left.

Step 5: Write the Final Answer

Once we’ve gone through all the terms, we write the final answer in the same format as the original equation. In our example, we get the quotient x² + 2x + 1 and the remainder 0.

For instance, let’s consider another polynomial: (6×3 + 7×2 + 3x – 5) ÷ (2x – 1).
We follow the above steps, and the final answer will be (3x² + 5x + 4) with a remainder of -1.

Step 6: Double Chech Your Answers

To verify if the result is correct, multiply the quotient by the divisor and add the remainder. The result should match the dividend.

If you want to explore more about doing long division with polynomials, I encourage you to check out Khan Academy or watch this video or the video below.

What to read next:

• Finding the Equation of a Tangent Line with Derivatives.
• How to Factor Out a Number From An Expression: Step by Step!
• Solving Systems of Equations by Substitution Method.

Wrapping Up

By following the six outlined in this article, you can perfect your long division with polynomials. While it may take time and patience, once you have mastered doing long division with polynomials, it can prove incredibly useful in solving more complex mathematical problems.

Remember to stay focused and take your time. I encourage you to review the steps discussed in this article as you practice.