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 Page 1


  
 
 
Factorisation 
Points to Remember 
? When we factorize an algebraic expression, we write it as a product of its factors. 
These factors are either numbers or algebraic variables or algebraic expressions. 
? We use following methods of factorisation: 
? Method of common factors 
? Regrouping method 
? Factorisation using following identities: 
? ?? ?? + ?????? + ?? ?? = (?? + ?? )
?? 
? ?? ?? - ?????? + ?? ?? = (?? - ?? )
?? 
? ?? ?? - ?? ?? = (?? - ?? )(?? + ?? ) 
? ?? ?? + (?? + ?? )?? + ???? = (?? + ?? )(?? + ?? ) 
? An irreducible factor is a factor which cannot be expressed further as a product 
of factors (i.e. prime factor for numbers) eg. ?? + ?? , ?? + ?? , ?? - ?? etc. 
? The general relation for division is: 
???????????????? = ?????????????? × ???????????????? + ???????????????? ?? 
? If Remainder = 0, then divisor is a factor of dividend. Eg.
?? ?? +???? +?? ?? +?? = 
(?? +?? )
?? ?? +?? = ?? + ?? 
? The degree of a polynomial is the highest power of its variables.e.g. the degree of 
the polynomial ?? ?? + ?? ?? ?? - ???? + ?? is 3 
 
QUESTIONS: 
1. What is the degree of algebraic expression ?? ?? + ???? + ?? ? 
2. If ?? +
?? ?? = v?? , what is the value of ?? ?? +
?? ?? ?? ? 
3. What is the quotient, when we divide ???????? ???? ???? ? 
4. If ?????? is one of the factor of (?? ?? ?? ?? + ?? ????
?? ), what is the other factor ?  
5. What is the HCF of ???? ?? ?? ?? ?? , ???? ?? ?? ?? ?? , ???? ?? ????
?? ?? ?  
6. What is the degree of the quotient of  
(?? ????
?? -???? ?? ?? )
????
 ?  
Page 2


  
 
 
Factorisation 
Points to Remember 
? When we factorize an algebraic expression, we write it as a product of its factors. 
These factors are either numbers or algebraic variables or algebraic expressions. 
? We use following methods of factorisation: 
? Method of common factors 
? Regrouping method 
? Factorisation using following identities: 
? ?? ?? + ?????? + ?? ?? = (?? + ?? )
?? 
? ?? ?? - ?????? + ?? ?? = (?? - ?? )
?? 
? ?? ?? - ?? ?? = (?? - ?? )(?? + ?? ) 
? ?? ?? + (?? + ?? )?? + ???? = (?? + ?? )(?? + ?? ) 
? An irreducible factor is a factor which cannot be expressed further as a product 
of factors (i.e. prime factor for numbers) eg. ?? + ?? , ?? + ?? , ?? - ?? etc. 
? The general relation for division is: 
???????????????? = ?????????????? × ???????????????? + ???????????????? ?? 
? If Remainder = 0, then divisor is a factor of dividend. Eg.
?? ?? +???? +?? ?? +?? = 
(?? +?? )
?? ?? +?? = ?? + ?? 
? The degree of a polynomial is the highest power of its variables.e.g. the degree of 
the polynomial ?? ?? + ?? ?? ?? - ???? + ?? is 3 
 
QUESTIONS: 
1. What is the degree of algebraic expression ?? ?? + ???? + ?? ? 
2. If ?? +
?? ?? = v?? , what is the value of ?? ?? +
?? ?? ?? ? 
3. What is the quotient, when we divide ???????? ???? ???? ? 
4. If ?????? is one of the factor of (?? ?? ?? ?? + ?? ????
?? ), what is the other factor ?  
5. What is the HCF of ???? ?? ?? ?? ?? , ???? ?? ?? ?? ?? , ???? ?? ????
?? ?? ?  
6. What is the degree of the quotient of  
(?? ????
?? -???? ?? ?? )
????
 ?  
  
 
7. What is the common factor of ???? + ???? ?????? ?? (?? + ?? ) ?  
8. Factorise: ?? ?? - ??????
?? 
9. Simplify: 
?????????? 
????
 
10. What should be added to ???? ?? ?? + ?? to make it (?? ?? - ?? )
?? ? 
11. Which identity will be used to factorise ?? ?? + ?????? + ?????? ?  
12. Find the value of (?????? × ?????? - ?? × ?? )  
13. What will be the product of (???? + ?? )(???? - ?? ) ?  
14. What will be the quotient on dividing ?? ?? - ?? - ???? by (?? - ?? )?  
15. What will be the common factor of (?? + ?? )( ?? + ?? )?????? ?? (?? + ?? ) ?  
16. What should be added to the left hand side to rectify the equation 
???? + ?? = ?? (?? + ?? ) 
17. What is the remainder when divisor is a factor of the dividend?  
18. Factorising ?????? ?? ?? - ???? ?? ?? gives ???? ?? ?? - ?? ?? ?? as one factor, what is the other 
factor? 
19. Simplify: 
?? ?? -????
(?? ?? +?? )(?? -?? )
 
20. Find the value of (?????? )
?? 
21. Evaluate: ???? × ?????? 
22. Factorise: ?? (?? - ?? ) + ?? (?? - ?? ) 
23. If ?? = ?? , ?? = ?? , find ?? ?? - ?? ?? 
24. What will be the coefficient of ?? ?? in the quotient of algebraic expression 
????
?? +?? ?? ?? +?? ?? +??  
25. What will be the quotient of algebraic expression 
?? ?? ?? ?? +?? ?? ?? ?? ?? -???????? ?? ?????? ? 
26. What will be the coefficient of ?? ?? in the product of (
?? ?? ?? ?? + ?? ?? ) (?? ?? -
?? ?? ?? ?? ) ?  
27. The area of a playground is (???? ?? ?? - ?????? ) square units and one of its side’s 
measures ???? units. What is the measure of the other side? 
28. If (???? ?? ?? + ?????? + ???? ) kilograms of sugar is stored in 7 bags in equal quantities, 
how many kilograms of sugar is there in each bag? 
29. What will be the constant term in the product of (?? + ?? )(?? - ?? ) ? 
30. Find ?? ?? - ?? ?? if ?? = -?? and ?? = ??  
31. Find (???? × ???? - ?? × ?? ) 
Page 3


  
 
 
Factorisation 
Points to Remember 
? When we factorize an algebraic expression, we write it as a product of its factors. 
These factors are either numbers or algebraic variables or algebraic expressions. 
? We use following methods of factorisation: 
? Method of common factors 
? Regrouping method 
? Factorisation using following identities: 
? ?? ?? + ?????? + ?? ?? = (?? + ?? )
?? 
? ?? ?? - ?????? + ?? ?? = (?? - ?? )
?? 
? ?? ?? - ?? ?? = (?? - ?? )(?? + ?? ) 
? ?? ?? + (?? + ?? )?? + ???? = (?? + ?? )(?? + ?? ) 
? An irreducible factor is a factor which cannot be expressed further as a product 
of factors (i.e. prime factor for numbers) eg. ?? + ?? , ?? + ?? , ?? - ?? etc. 
? The general relation for division is: 
???????????????? = ?????????????? × ???????????????? + ???????????????? ?? 
? If Remainder = 0, then divisor is a factor of dividend. Eg.
?? ?? +???? +?? ?? +?? = 
(?? +?? )
?? ?? +?? = ?? + ?? 
? The degree of a polynomial is the highest power of its variables.e.g. the degree of 
the polynomial ?? ?? + ?? ?? ?? - ???? + ?? is 3 
 
QUESTIONS: 
1. What is the degree of algebraic expression ?? ?? + ???? + ?? ? 
2. If ?? +
?? ?? = v?? , what is the value of ?? ?? +
?? ?? ?? ? 
3. What is the quotient, when we divide ???????? ???? ???? ? 
4. If ?????? is one of the factor of (?? ?? ?? ?? + ?? ????
?? ), what is the other factor ?  
5. What is the HCF of ???? ?? ?? ?? ?? , ???? ?? ?? ?? ?? , ???? ?? ????
?? ?? ?  
6. What is the degree of the quotient of  
(?? ????
?? -???? ?? ?? )
????
 ?  
  
 
7. What is the common factor of ???? + ???? ?????? ?? (?? + ?? ) ?  
8. Factorise: ?? ?? - ??????
?? 
9. Simplify: 
?????????? 
????
 
10. What should be added to ???? ?? ?? + ?? to make it (?? ?? - ?? )
?? ? 
11. Which identity will be used to factorise ?? ?? + ?????? + ?????? ?  
12. Find the value of (?????? × ?????? - ?? × ?? )  
13. What will be the product of (???? + ?? )(???? - ?? ) ?  
14. What will be the quotient on dividing ?? ?? - ?? - ???? by (?? - ?? )?  
15. What will be the common factor of (?? + ?? )( ?? + ?? )?????? ?? (?? + ?? ) ?  
16. What should be added to the left hand side to rectify the equation 
???? + ?? = ?? (?? + ?? ) 
17. What is the remainder when divisor is a factor of the dividend?  
18. Factorising ?????? ?? ?? - ???? ?? ?? gives ???? ?? ?? - ?? ?? ?? as one factor, what is the other 
factor? 
19. Simplify: 
?? ?? -????
(?? ?? +?? )(?? -?? )
 
20. Find the value of (?????? )
?? 
21. Evaluate: ???? × ?????? 
22. Factorise: ?? (?? - ?? ) + ?? (?? - ?? ) 
23. If ?? = ?? , ?? = ?? , find ?? ?? - ?? ?? 
24. What will be the coefficient of ?? ?? in the quotient of algebraic expression 
????
?? +?? ?? ?? +?? ?? +??  
25. What will be the quotient of algebraic expression 
?? ?? ?? ?? +?? ?? ?? ?? ?? -???????? ?? ?????? ? 
26. What will be the coefficient of ?? ?? in the product of (
?? ?? ?? ?? + ?? ?? ) (?? ?? -
?? ?? ?? ?? ) ?  
27. The area of a playground is (???? ?? ?? - ?????? ) square units and one of its side’s 
measures ???? units. What is the measure of the other side? 
28. If (???? ?? ?? + ?????? + ???? ) kilograms of sugar is stored in 7 bags in equal quantities, 
how many kilograms of sugar is there in each bag? 
29. What will be the constant term in the product of (?? + ?? )(?? - ?? ) ? 
30. Find ?? ?? - ?? ?? if ?? = -?? and ?? = ??  
31. Find (???? × ???? - ?? × ?? ) 
  
 
32. Find ?? if ?? (?? ?? - ?? ?? ) = ?? ?? - ?? ?? 
33. Find ?? if ?? (?? ?? + ?? ?? ) = ?? ?? - ?? ?? 
34. What are the prime factors of ???? ?  
35. Simplify: ?? ?? - ?? × ?? × ?? + ?? ?? 
36. What will be the two numbers ?? and ?? such that ?? - ?? = ?? and ???? = ???? ? 
37. Evaluate: (?? . ?? )
?? – (?? . ?? )
?? 
38. If ???? + ???? = ???? and ???? - ???? = ???? , find ?? . 
39. Simplify: 
(?? +?? )
?? -(?? -?? )
?? ????
 
40. Find ???????????????? when ???? ?? ???????? = ?? + ?? , ???????????????? = ?? + ?? and ?????????????????? =
?? 
41. Find ???????????????? if ???????????????? = ?? ?? , ?????????????? = ?? - ?? and ?????????????????? = ???? 
42. If ?? - 
?? ?? = ?? , find ?? ?? +
?? ?? ?? ? 
43. If ?? + 
?? ?? = ???? , find ?? ?? +
?? ?? ?? ? 
44. Express ?? ?? + ???? + ???? as product of two expressions. 
45. Simplify: 
(?? ?? +?? ?? )
(?? ?? -?? ?? )
 
46. Evaluate: 
?? .?? ×(?? +?? .?? )
?? +?? .?? 
47. Evaluate: (?? . ?? )
?? - (?? . ?? )
?? 
48. What will be the value of  ?? ?? + ?? ?? - ?? + ?? ???? ?? = ?? ? 
49. What will be the value of  ?? ?? - ?? ?? + ?? + ?? ???? ?? = -?? ? 
50. Evaluate: 
?? .?? ×?? .?? ???? -?? .?? 
  
Page 4


  
 
 
Factorisation 
Points to Remember 
? When we factorize an algebraic expression, we write it as a product of its factors. 
These factors are either numbers or algebraic variables or algebraic expressions. 
? We use following methods of factorisation: 
? Method of common factors 
? Regrouping method 
? Factorisation using following identities: 
? ?? ?? + ?????? + ?? ?? = (?? + ?? )
?? 
? ?? ?? - ?????? + ?? ?? = (?? - ?? )
?? 
? ?? ?? - ?? ?? = (?? - ?? )(?? + ?? ) 
? ?? ?? + (?? + ?? )?? + ???? = (?? + ?? )(?? + ?? ) 
? An irreducible factor is a factor which cannot be expressed further as a product 
of factors (i.e. prime factor for numbers) eg. ?? + ?? , ?? + ?? , ?? - ?? etc. 
? The general relation for division is: 
???????????????? = ?????????????? × ???????????????? + ???????????????? ?? 
? If Remainder = 0, then divisor is a factor of dividend. Eg.
?? ?? +???? +?? ?? +?? = 
(?? +?? )
?? ?? +?? = ?? + ?? 
? The degree of a polynomial is the highest power of its variables.e.g. the degree of 
the polynomial ?? ?? + ?? ?? ?? - ???? + ?? is 3 
 
QUESTIONS: 
1. What is the degree of algebraic expression ?? ?? + ???? + ?? ? 
2. If ?? +
?? ?? = v?? , what is the value of ?? ?? +
?? ?? ?? ? 
3. What is the quotient, when we divide ???????? ???? ???? ? 
4. If ?????? is one of the factor of (?? ?? ?? ?? + ?? ????
?? ), what is the other factor ?  
5. What is the HCF of ???? ?? ?? ?? ?? , ???? ?? ?? ?? ?? , ???? ?? ????
?? ?? ?  
6. What is the degree of the quotient of  
(?? ????
?? -???? ?? ?? )
????
 ?  
  
 
7. What is the common factor of ???? + ???? ?????? ?? (?? + ?? ) ?  
8. Factorise: ?? ?? - ??????
?? 
9. Simplify: 
?????????? 
????
 
10. What should be added to ???? ?? ?? + ?? to make it (?? ?? - ?? )
?? ? 
11. Which identity will be used to factorise ?? ?? + ?????? + ?????? ?  
12. Find the value of (?????? × ?????? - ?? × ?? )  
13. What will be the product of (???? + ?? )(???? - ?? ) ?  
14. What will be the quotient on dividing ?? ?? - ?? - ???? by (?? - ?? )?  
15. What will be the common factor of (?? + ?? )( ?? + ?? )?????? ?? (?? + ?? ) ?  
16. What should be added to the left hand side to rectify the equation 
???? + ?? = ?? (?? + ?? ) 
17. What is the remainder when divisor is a factor of the dividend?  
18. Factorising ?????? ?? ?? - ???? ?? ?? gives ???? ?? ?? - ?? ?? ?? as one factor, what is the other 
factor? 
19. Simplify: 
?? ?? -????
(?? ?? +?? )(?? -?? )
 
20. Find the value of (?????? )
?? 
21. Evaluate: ???? × ?????? 
22. Factorise: ?? (?? - ?? ) + ?? (?? - ?? ) 
23. If ?? = ?? , ?? = ?? , find ?? ?? - ?? ?? 
24. What will be the coefficient of ?? ?? in the quotient of algebraic expression 
????
?? +?? ?? ?? +?? ?? +??  
25. What will be the quotient of algebraic expression 
?? ?? ?? ?? +?? ?? ?? ?? ?? -???????? ?? ?????? ? 
26. What will be the coefficient of ?? ?? in the product of (
?? ?? ?? ?? + ?? ?? ) (?? ?? -
?? ?? ?? ?? ) ?  
27. The area of a playground is (???? ?? ?? - ?????? ) square units and one of its side’s 
measures ???? units. What is the measure of the other side? 
28. If (???? ?? ?? + ?????? + ???? ) kilograms of sugar is stored in 7 bags in equal quantities, 
how many kilograms of sugar is there in each bag? 
29. What will be the constant term in the product of (?? + ?? )(?? - ?? ) ? 
30. Find ?? ?? - ?? ?? if ?? = -?? and ?? = ??  
31. Find (???? × ???? - ?? × ?? ) 
  
 
32. Find ?? if ?? (?? ?? - ?? ?? ) = ?? ?? - ?? ?? 
33. Find ?? if ?? (?? ?? + ?? ?? ) = ?? ?? - ?? ?? 
34. What are the prime factors of ???? ?  
35. Simplify: ?? ?? - ?? × ?? × ?? + ?? ?? 
36. What will be the two numbers ?? and ?? such that ?? - ?? = ?? and ???? = ???? ? 
37. Evaluate: (?? . ?? )
?? – (?? . ?? )
?? 
38. If ???? + ???? = ???? and ???? - ???? = ???? , find ?? . 
39. Simplify: 
(?? +?? )
?? -(?? -?? )
?? ????
 
40. Find ???????????????? when ???? ?? ???????? = ?? + ?? , ???????????????? = ?? + ?? and ?????????????????? =
?? 
41. Find ???????????????? if ???????????????? = ?? ?? , ?????????????? = ?? - ?? and ?????????????????? = ???? 
42. If ?? - 
?? ?? = ?? , find ?? ?? +
?? ?? ?? ? 
43. If ?? + 
?? ?? = ???? , find ?? ?? +
?? ?? ?? ? 
44. Express ?? ?? + ???? + ???? as product of two expressions. 
45. Simplify: 
(?? ?? +?? ?? )
(?? ?? -?? ?? )
 
46. Evaluate: 
?? .?? ×(?? +?? .?? )
?? +?? .?? 
47. Evaluate: (?? . ?? )
?? - (?? . ?? )
?? 
48. What will be the value of  ?? ?? + ?? ?? - ?? + ?? ???? ?? = ?? ? 
49. What will be the value of  ?? ?? - ?? ?? + ?? + ?? ???? ?? = -?? ? 
50. Evaluate: 
?? .?? ×?? .?? ???? -?? .?? 
  
  
 
ANSWERS 
Question 
No. 
Answer 
Question  
No. 
Answer 
1 ?? 26 
?? ?? 
2 ?? 27 (???? - ?? ) ?????????? 
3 ???? 28 (?? ?? ?? + ???? + ?? ) ?????????????????? 
4 ?? + ?? 29 -???? 
5 ?? ?? ?? ?? ?? 30 ?? 
6 ?? 31 ???? 
7 ?? + ?? 32 ?? ?? + ?? ?? 
8 ?? ?? (?? ?? - ???? ) 33 ?? ?? - ?? ?? 
9 ???????? 34 ?? , ?? 
10 -?????? 35 ?? 
11 (?? + ?? )
?? = ?? ?? + ?????? + ?? ?? 36 ?? = ?? , ?? = ?? 
12 ?????????? 37 ?? 
13 ?? ?? ?? - ?? 38 ?? = ?? 
14 ?? + ?? 39 ?? 
15 ?? + ?? 40 ?? ?? + ???? + ?? 
16 ?? 41 ?? + ?? 
17 ?? 42 ???? 
18 ???? ?? ?? + ?? ?? ?? 43 ?????? 
19 ?? + ?? 44 (?? + ?? )(?? + ?? ) 
20 ?????????? 45 
?? ?? ?? - ?? ?? ???? 
?? (?? + ?? )(?? - ?? )
 
21 ???????? 46 ?? . ?? 
22 (?? + ?? )(?? - ?? ) 47 ???? 
23 ???? 48 ?? 
24 ?? 49 -?? 
25 ?? + ?????? - ???? 50 ?? . ??

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Document Description: Mental Maths Questions and Answers: Factorisation for Class 8 2024 is part of Mental Mathematics for Class 8 preparation. The notes and questions for Mental Maths Questions and Answers: Factorisation have been prepared according to the Class 8 exam syllabus. Information about Mental Maths Questions and Answers: Factorisation covers topics like and Mental Maths Questions and Answers: Factorisation Example, for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Mental Maths Questions and Answers: Factorisation.

Introduction of Mental Maths Questions and Answers: Factorisation in English is available as part of our Mental Mathematics for Class 8 for Class 8 & Mental Maths Questions and Answers: Factorisation in Hindi for Mental Mathematics for Class 8 course. Download more important topics related with notes, lectures and mock test series for Class 8 Exam by signing up for free. Class 8: Mental Maths Questions and Answers: Factorisation | Mental Mathematics for Class 8

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