Long Division | How to Divide Polynomials | Grade 10 Math @MathTeacherGon

Summary

In this video, the teacher provides a step-by-step guide on dividing polynomials using long division. The process begins by dividing the first term of the dividend by the first term of the divisor, followed by multiplication, subtraction, and bringing down the next terms. The video uses an example involving two polynomials: a divisor (2x + 1) and a dividend (4x³ - 8x² + 7x - 11). The teacher explains each step clearly, ensuring students understand the concept of the quotient and remainder. The lesson concludes with the final expression of the quotient and remainder, encouraging viewers to like and subscribe for more educational content.

Takeaways

• 😀 The lesson focuses on dividing polynomials using long division, a method distinct from synthetic division.
• 😀 The first polynomial (dividend) is 4x³ - 8x² + 7x - 1, and the second (divisor) is 2x + 1.
• 😀 The first step in long division is to divide the first term of the dividend by the first term of the divisor.
• 😀 4x³ ÷ 2x equals 2x², which is the first term of the quotient.
• 😀 Next, multiply the quotient term (2x²) by the entire divisor (2x + 1), and subtract the result from the dividend.
• 😀 After subtraction, bring down the next term and repeat the division process with the new polynomial.
• 😀 In the second step, divide -10x² by 2x, which gives -5x, and multiply this by the divisor.
• 😀 Continue subtracting and bringing down terms as the process moves forward.
• 😀 The final quotient is 2x² - 5x + 6, and the remainder is -17.
• 😀 The final result of the division is expressed as the quotient plus the remainder over the divisor.
• 😀 The teacher encourages viewers to subscribe to the channel for more educational content.

Q & A

What is the main topic discussed in the video?

The main topic discussed in the video is how to divide polynomials using long division.

What are the two polynomials used in the example?

The two polynomials used in the example are 2x + 1 (divisor) and 4x³ - 8x² + 7x - 1 (dividend).

What is the first step in dividing polynomials using long division?

The first step is to divide the first term of the dividend (4x³) by the first term of the divisor (2x).

How do you handle the multiplication step in long division?

You multiply the term obtained from the division (in this case, 2x²) by the entire divisor (2x + 1) to get the result.

Why do we subtract after multiplying the terms?

We subtract to eliminate the matching terms from the dividend, as part of the long division process.

What do you do after subtracting the terms and getting a remainder?

After subtracting, bring down the next term from the dividend and repeat the division and multiplication process.

What happens when you reach the final term in the division?

When you reach the final term, you subtract once again and are left with a remainder, which is included in the final answer.

What is the quotient from the division in this example?

The quotient is 2x² - 5x + 6.

What is the remainder in this example?

The remainder is -17.

How do you express the final result of the division?

The final result is expressed as the quotient (2x² - 5x + 6) plus the remainder (-17) over the divisor (2x + 1), so the answer is (2x² - 5x + 6) + (-17)/(2x + 1).