Remainder theorem and factor theorem — methodical recommendation. Mathematics State Board, Class 9.

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Methodical recommendation:

Theory

Number	Name	Description
1.	Remainder theorem	To learn how to find the factors using remainder theorem.
2.	Factor theorem	To learn and understand the factor theorem.
3.	Mind map	Try to learn the concept on how to find the remainder and factors of the polynomial.

Textbook Questions

Number	Name	Type	Difficulty	Marks	Description
1.	Multiple choice questions I	Other	easy	3 m.	Select the suitable choice for the given questions.
2.	Multiple choice questions II	Other	easy	3 m.	Select the correct choice for the given questions.
3.	Two mark example problems I	Other	easy	6 m.	Try to answer the given questions.
4.	Two mark example problems - II	Other	easy	6 m.	Try to answer the questions by using factor theorem.
5.	Two mark example problems - III	Other	easy	2 m.	Try to find the value of the variable.
6.	Two mark exercise problems I	Other	medium	6 m.	Try to answer the given questions.
7.	Two mark exercise problems II	Other	medium	6 m.	Try to find the remainder of the given polynomials.
8.	Two mark exercise problems III	Other	medium	6 m.	Check your understanding skills in the concept of finding remainder and factor.
9.	Two mark exercise problems IV	Other	medium	8 m.	Try to answer the given questions.
10.	Five mark example problems	Other	hard	5 m.	Check your understanding skills in the concept of remainder theorem.
11.	Five mark exercise problems I	Other	hard	5 m.	Try to answer the given questions.
12.	Five mark exercise problems II	Other	hard	0 m.	Try to verify the given using factor theorem.

Practice Questions

Number	Name	Type	Difficulty	Marks	Description
1.	Select the correct remainder of the polynomial	Other	easy	2 m.	Practice to find the remainder of the polynomial using remainder theorem.
2.	Determine the value of 'k'	Other	easy	2 m.	Try using the factor theorem to predict the unknown value of 'k'.
3.	Pick the remainder of the polynomial	Other	medium	2 m.	Practice to find the remainder of the polynomial.
4.	Find the unknown	Other	medium	2 m.	To find the unknown co-efficient of the variable of the given polynomial using factor theorem.
5.	Classify the divisor is a factor or not	Other	medium	2 m.	Try to check whether the given divisor is a factor of the polynomial.
6.	Find an unknown value for 'k'	Other	medium	2 m.	Try seeking the unknown value of 'k'.
7.	Identify the correct remainder	Other	hard	5 m.	Practice to find the remainder of the polynomial by applying remainder theorem.
8.	Predict the remainder if the polynomial is divided by factor	Other	hard	5 m.	Try to find out the remainder of the polynomial when it is divided by a factor.
9.	Check the dimension	Other	hard	5 m.	Application to practise factor theorem of the polynomials.

Key Questions for School Exam Preparation

Number	Name	Type	Difficulty	Marks	Description
1.	Verify whether the given is a factor of the polynomial	Other	easy	2 m.	Try to answer the questions by using factor theorem.
2.	Check whether (p(x) is a multiple of (g(x))	Other	medium	2 m.	Try to answer the given questions.
3.	Find the value of 'm'	Other	medium	2 m.	Try to answer the given questions.
4.	Determine the remainder	Other	medium	2 m.	Try to find the remainder of the given polynomial.

Questions for Teacher Use

Number	Name	Type	Difficulty	Marks	Description
1.	Find out the remainder	Other	easy	2 m.	Try to find the remainder of the polynomial with the help of remainder theorem.
2.	Predict the remainder of the polynomial	Other	medium	2 m.	It is required to select the correct remainder of the polynomial when it is divided by the given factor.
3.	Check whether the divisor is a factor of the polynomial.	Other	medium	2 m.	Endeavor and see whether the divisor is a factor of the polynomial.
4.	Verify whether the given divisor is a factor	Other	medium	2 m.	See whether the given divisor is a factor of the polynomial.
5.	Get the remainder when polynomial is divided by a factor	Other	hard	5 m.	Practice to find the remainder if the polynomial is divided by a factor.
6.	Applying the remainder theorem find the value of 'k'	Other	easy	2 m.	Try to find the value of the variable.
7.	Find the remainder	Other	medium	2 m.	Try to answer the given questions.
8.	Length of the rectangle	Other	medium	2 m.	Check your understanding skills in the concept of division algorithm of polynomials.

Periodic assessments

Number	Name	Recomended time:	Difficulty	Marks	Description
1.	Homework I	00:15:00	easy	10 m.
2.	Homework II	00:15:00	easy	10 m.
3.	Homework III	00:15:00	medium	10 m.
4.	Homework IV	00:20:00	medium	14 m.
5.	Revision test I	00:25:00	medium	16 m.
6.	Revision test II	00:25:00	hard	20 m.
7.	Revision test III	00:35:00	hard	24 m.
8.	Periodic Assessment	00:10:00	medium	6 m.	PA 1 - Remainder theorem and factor theorem

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