How to Divide Polynomials Using Long Division

TL;DR

To divide polynomials using long division, start by setting up the divisor outside and the dividend inside. Divide the leading term of the dividend by the leading term of the divisor, multiply the divisor by this result, subtract, and repeat until you reach a remainder. This method allows you to find both the quotient and any leftover terms that couldn't be divided evenly.

Transcript

in this video we're going to talk about how to use long division with polynomials now i recommend that you watch this video from beginning to end because i'm going to start with some easy problems and then progressively it's going to get harder and harder so let's begin let's say if we want to divide x squared plus 9x plus 20 by x plus 5. how can w... Read More

Key Insights

• 🪘 Long division with polynomials involves dividing, multiplying, and subtracting to find the quotient and remainder.
• 🍉 Each term in the divisor is used to divide the corresponding terms in the dividend.
• ➗ The remainder in polynomial long division represents any remaining terms that couldn't be divided evenly.
• 💦 Checking your work by multiplying the quotient and divisor can help ensure accuracy and correctness.
• 🤩 Practice and familiarity with the process are key to successfully using long division with polynomials.
• 🍉 The degree of the terms in the divisor should match or be lower than the degree of the terms in the dividend.
• 😫 Setting up the problem correctly and organizing the steps can make the long division process easier to follow.

Questions & Answers

Q: What is the first step in long division with polynomials?

The first step in long division with polynomials is to set up the problem with the dividend and divisor written out, similar to regular long division with numbers.

Q: How do you find the next term in the quotient?

To find the next term in the quotient, divide the highest degree term in the dividend by the highest degree term in the divisor. This term becomes the next term in the quotient.

Q: What is the significance of the remainder in polynomial long division?

The remainder in polynomial long division represents any terms that can't be divided evenly. It is included in the final answer as part of the quotient.

Q: How can you check your work in polynomial long division?

You can check your work by multiplying the quotient and divisor together. If you get the original dividend, then your division was done correctly.

Summary & Key Takeaways

• The video provides step-by-step instructions on how to use long division with polynomials.

• The process involves dividing, multiplying, and subtracting to find the quotient and remainder.

• Several examples are demonstrated, showing how to divide different polynomials using long division.