The long division method is a systematic procedure used to divide one polynomial expression by another, similar to the long division method for dividing integers. This method is particularly useful when dealing with polynomial division where the divisor is of a higher degree than the dividend. Here's a description of the long division method for polynomials: Setup: Write the dividend (the polynomial being divided) inside the division bracket, and write the divisor (the polynomial dividing the dividend) outside the bracket, just like regular long division. Division: Start by dividing the leading term of the dividend by the leading term of the divisor. Write the result above the division bracket. Multiplication: Multiply the entire divisor by the quotient obtained in the previous step. Subtraction: Subtract the result obtained in the previous step from the dividend. Write the result below the division bracket, aligning like terms. Repeat: If the degree of the resulting polynomial after subtraction is still greater than or equal to the degree of the divisor, repeat steps 2 through 4 with the new polynomial. Otherwise, the division is complete. Finalize: Once the degree of the resulting polynomial is less than the degree of the divisor, the process is complete. The quotient obtained through the division represents the result of the division, and any remainder, if present, can also be written down. Check: It's always a good practice to verify the division by multiplying the quotient with the divisor and adding any remainder obtained. The result should match the original dividend. The long division method provides a structured approach to polynomial division, ensuring accuracy and efficiency in obtaining the quotient and remainder. It's a fundamental technique used in algebra and calculus, particularly in simplifying complex expressions, solving equations, and finding roots of polynomials. The long division method for polynomials provides a systematic approach to division, ensuring that each step is carried out accurately. It's an essential technique in algebra for simplifying polynomial expressions, finding roots, and solving equations.

2. AT THE END OF THIS LESSON, THE STUDENTS WOULD BE ABLE TO :
Identify the dividend, divisor,
quotient and remainder in
polynomials long division problems
divide polynomial in one variable
using Long Division

3. Identify whether each algebraic expression is a Polynomial or Not
Polynomial.

4. Find each product.

9. Example 1 Divide 𝑥2
+ 4𝑥 − 21 𝑏𝑦 𝑥 − 3

10. Example 1 Divide 𝑥2
+ 4𝑥 − 21 𝑏𝑦 𝑥 − 3

11. Example 1 Divide 𝑥2
+ 4𝑥 − 21 𝑏𝑦 𝑥 − 3

12. Example 1 Divide 𝑥2
+ 4𝑥 − 21 𝑏𝑦 𝑥 − 3

13. Example 2 Divide 𝑥3
+ 6𝑥2
+ 13𝑥 + 12 𝑏𝑦 𝑥 − 3

14. Example 2 Divide 𝑥3
+ 6𝑥2
+ 13𝑥 + 12 𝑏𝑦 𝑥 − 3

15. Example 2 Divide 𝑥3
+ 6𝑥2
+ 13𝑥 + 12 𝑏𝑦 𝑥 − 3

16. Example 2 Divide 𝑥3
+ 6𝑥2
+ 13𝑥 + 12 𝑏𝑦 𝑥 − 3

17. Example 2 Divide 𝑥3
+ 6𝑥2
+ 13𝑥 + 12 𝑏𝑦 𝑥 − 3

18. Example 2 Divide 𝑥3
+ 6𝑥2
+ 13𝑥 + 12 𝑏𝑦 𝑥 − 3

19. Example 2 Divide 𝑥3
+ 6𝑥2
+ 13𝑥 + 12 𝑏𝑦 𝑥 − 3

37. 50,000
1,850,000 150,200 75,000
1,850isthebiggestnumber. Itisinthefirstposition.
50,000isthesmallestnumber. Itisinthelastposition.
Wewritethenumbersinthedecreasingorderas
follows:
Towritenumbersindescendingorder,wearrangethemfrombiggesttosmallest.

38. Elementary Math