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Division of polynomials and GCD

Methodical recommendation:

Theory

Number Name Description
1. Division algorithm for polynomials Learn to find the remainder and quotient using long division method.
2. Synthetic division To learn the process of synthetic division to find the roots of the polynomial.
3. Factorisation using synthetic division To learn how to factorise a cubic polynomial by synthetic division method.
4. GCD of a polynomial Leard how to find the GCD of polynomial by factorisation.
5. Mind map Mind map of the representation of division of polynomials and factorization of polynomials.

Textbook Questions

Number Name Type Difficulty Marks Description
1. Multiple choice questions Other easy 2 m. Select the suitable choice for the given questions.
2. Two mark example problems I Other easy 4 m. Try to divide using division algorithm of polynomials.
3. Two mark example problems II Other easy 4 m. Check your understanding skills in the concept of synthetic division.
4. Two mark example problems III Other easy 4 m. Check your understanding skills in the concept of factorization.
5. Two mark example problems IV Other easy 6 m. Try to find the GCD of the polynomials.
6. Two mark exercise problems I Other easy 4 m. Try to divide using division algorithm of polynomials.
7. Two mark exercise problems II Other easy 4 m. Try to divide using division algorithm of polynomials.
8. Two mark exercise problems III Other easy 4 m. Check your understanding skills in the concept of synthetic division.
9. Two mark exercise problems IV Other medium 6 m. Try to answer the given questions.
10. Two mark exercise problems V Other medium 6 m. Check your understanding skills in the concept of GCD.
11. Two mark exercise problems VI Other medium 6 m. Check your understanding skills in the concept of GCD.
12. Two mark exercise problems VII Other medium 6 m. Check your understanding skills in the concept of GCD.
13. Two mark exercise problems VIII Other medium 6 m. Check your understanding skills in the concept of GCD.
14. Five mark example problems I Other medium 5 m. Try to factorise the given expression.
15. Five mark example problems II Other medium 5 m. Try to factorize the given expression.
16. Five mark example problems III Other medium 10 m. Try to divide using division algorithm of polynomials.
17. Five mark example problems IV Other medium 10 m. Check your understanding skills in the concept of synthetic division.
18. Five mark exercise problems I Other medium 10 m. Check your understanding skills in the concept of division algorithm of polynomials.
19. Five mark exercise problems II Other hard 10 m. Try to answer the given questions.
20. Five mark exercise problem III Other hard 10 m. Check your understanding skills in the concept of synthetic division.
21. Five mark exercise problems IV Other hard 10 m. Try to answer the given questions.
22. Five mark exercise problems V Other hard 10 m. Try to answer the given questions.
23. Five mark exercise problems VI Other hard 10 m. Try to answer the given questions.

Practice Questions

Number Name Type Difficulty Marks Description
1. Say true or false Other easy 1 m. To check whether the given linear polynomial is a factor of the polynomial 'p(x)'.
2. Complete the sentence Other easy 2 m. To check whether the given linear polynomial is a factor of the polynomial 'p(x)'.
3. Divide the polynomial by monomial Other easy 2 m. Practice to divide a polynomial by a monomial.
4. Find the remainder when polynomial is divided by its factor Other easy 2 m. Practice to find the remainder of the polynomial when its factor is given.
5. Find the GCD Other medium 2 m. To practise how to find the GCD of the given polynomial.
6. Express the remainder by long division method Other medium 2 m. Attempt to find the remainder with the help of long division method.
7. Find the quotient Other medium 2 m. To find the quotient of a polynomial using synthetic division.
8. Find the remainder Other medium 2 m. To find the remainder of a polynomial using synthetic division.
9. Find out the factors Other medium 2 m. To find out the linear factors of the cubic polynomial using synthetic division.
10. Factorise the polynomial Other hard 5 m. To factorise the cubic polynomial into linear factors using synthetic division.
11. Calculate the remainder using long division method Other hard 5 m. Practice to find the remainder of the higher degree polynomial using long division method.
12. Find the remainder and quotient Other hard 5 m. Practice to find the remainder and the quotient when the polynomial is divided by binomial.

Key Questions for School Exam Preparation

Number Name Type Difficulty Marks Description
1. Determine the GCD Other easy 2 m. Check your understanding skills in the concept of GCD.
2. Find the quotient and remainder Other easy 2 m. Try to divide using division algorithm of polynomials.
3. Find the quotient and remainder using synthetic division Other medium 2 m. Check your understanding skills in the concept of synthetic division.
4. Determine the quotient and remainder by long division method Other medium 5 m. Try to divide using division algorithm of polynomials.
5. Determine the height of the parallelogram Other medium 5 m. Check your understanding skills in the concept of division algorithm of polynomials.
6. Find the value of p,q and remainder Other hard 5 m. Try to answer the given questions.
7. Factorize the expression Other hard 5 m. Try to answer the given questions.

Questions for Teacher Use

Number Name Type Difficulty Marks Description
1. Choose the best option Other easy 1 m. To check the factor of a quadratic polynomial using synthetic division.
2. Divide the polynomial by monomial Other easy 2 m. It is required to divide the polynomial by a monomial.
3. Divide the polynomial Other medium 2 m. Practice to divide the polynomial by binomial using long division method.
4. Find the quotient and the remainder Other medium 2 m. To find the quotient of a polynomial using synthetic division.
5. Prove the statement Other medium 5 m. To check whether (x-1) is a factor of the given polynomial series.
6. Activity! Other hard 5 m. To learn the concept of GCD based on a class room activity.
7. Find the value of 'a' and 'b' Other hard 5 m. To factorise the cubic polynomial and find the values of 'a' and 'b' using synthetic division.
8. Find the GCD Other medium 2 m. To practise how to find the GCD of the given polynomial.

Periodic assessments

Number Name Recomended time: Difficulty Marks Description
1. Homework I 00:15:00 easy 8 m.
2. Homework II 00:15:00 easy 10 m.
3. Homework III 00:15:00 easy 10 m.
4. Homework IV 00:20:00 easy 16 m.
5. Homework V 00:25:00 medium 17 m.
6. Homework VI 00:25:00 medium 20 m.
7. Revision test I 00:25:00 medium 20 m.
8. Revision test II 00:25:00 medium 21 m.
9. Revision test III 00:30:00 hard 24 m.
10. Revision test IV 00:30:00 hard 26 m.
11. Revision test V 00:35:00 hard 30 m.
12. Revision test VI 00:35:00 hard 30 m.
13. Periodic Assessment 00:10:00 medium 2 m. PA 1 - Algebraic identities
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