Вы находитесь на странице: 1из 1

# ASSIGNMENT-01

TOPIC-POLYNOMIALS

## 1. Evaluate: 101 99 using identities.

2. Find the remainder when 3 2 + 5 is divided by .
3. Find the value of + + , if + + = 9 and 2 + 2 + 2 = 35
4. Show that (2 + 1), ( 3) and (3 + 1) are factors of the polynomial
6 3 13 2 14 3.
5. Factorise: (3 + 4)2 + 2(3 + 4)(3 4) + (3 4)2
6. The polynomials () = 3 3 2 + 4 and () = 2 3 5 + when divided by
( 2) leaves remainder as and . If 2 = 4, find .
7. Prove that ( )3 + ( )3 + ( )3 3( )( )( ) = 0, when
+ + = 3.
8. Factorise: 2 3 9 2 + + 12
9. Factorise: 16 3 2 3
10. If + + 1 = 0, prove that 3 + 3 + 1 = 3.
11. Simplify: ( + + )2 + ( )2
12. If + 2 = 10, = 15, find 3 + 8 3
13. Factorise: ( 2 4)( 2 4 1) 20
14. 1 and 2 are the remainders obtained when 3+2257 and 3+212+6 are
divided by +1 and 2 respectively and if 212=6, then find thevalue of .
15. Factorise: (2 2)2 23(2 2) + 120
16. Using factor theorem, factorise: 3 2 2 5 + 6
17. Check if the polynomial () = 4 3 + 4 2 1 is exactly divisible by 2 + 1.
18. Evaluate 93 107 without multiplying directly.
2 2 2
19. If , , are all non zero and + + = 0, prove that: + + = 3
20. Find the value of so that (2 1) be the factor of 8 4 + 4 3 16 2 + 10 + .
1
21. If () = 2 4 + 3, evaluate (2) (1) + (2)
22. Factorise: 3 8 2 + 17 10
23. Factorise: 8( + )3 + 27( )3
24. Let 1 and 2 are the remainder when a polynomial 3 + 2 2 5 7 and
3 + 2 12 + 6 are divided by ( + 1) and ( 2) respectively. If 21 2=10,
find the value of .
25. If the polynomial () = 4 2 3 + 3 2 + 8 is divided by ( 2) leaves the
remainder 10, then find the value of .
26. Factorise: 3 3 2 10 + 24
1
27. Verify that: 3 + 3 + 3 3 = ( + + )[( )2 + ( )2 + ( )2 ]
2
28. Find the value of if the polynomial () = 4 2 3 + 3 2 + 3 7 when
divided by ( + 1) leaves the remainder 19. Also find the remainder when () is
divided by ( + 2).
29. The polynomials 3 + 32 3 and 23 5 + when divided by
4 leave the remainders 1 and 2 respectively, find the value of if 21 2 = 0.
3 3 3
30. If + + = 6 and + + = 11, find the value of + + 3.
The text passage is a list of mathematical problems, primarily focused on polynomials, identities, and factorization. Each problem is a distinct question, and no answers are provided within the text.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Вы находитесь на странице: 1из 1

# ASSIGNMENT-01

TOPIC-POLYNOMIALS

## 1. Evaluate: 101 99 using identities.

2. Find the remainder when 3 2 + 5 is divided by .
3. Find the value of + + , if + + = 9 and 2 + 2 + 2 = 35
4. Show that (2 + 1), ( 3) and (3 + 1) are factors of the polynomial
6 3 13 2 14 3.
5. Factorise: (3 + 4)2 + 2(3 + 4)(3 4) + (3 4)2
6. The polynomials () = 3 3 2 + 4 and () = 2 3 5 + when divided by
( 2) leaves remainder as and . If 2 = 4, find .
7. Prove that ( )3 + ( )3 + ( )3 3( )( )( ) = 0, when
+ + = 3.
8. Factorise: 2 3 9 2 + + 12
9. Factorise: 16 3 2 3
10. If + + 1 = 0, prove that 3 + 3 + 1 = 3.
11. Simplify: ( + + )2 + ( )2
12. If + 2 = 10, = 15, find 3 + 8 3
13. Factorise: ( 2 4)( 2 4 1) 20
14. 1 and 2 are the remainders obtained when 3+2257 and 3+212+6 are
divided by +1 and 2 respectively and if 212=6, then find thevalue of .
15. Factorise: (2 2)2 23(2 2) + 120
16. Using factor theorem, factorise: 3 2 2 5 + 6
17. Check if the polynomial () = 4 3 + 4 2 1 is exactly divisible by 2 + 1.
18. Evaluate 93 107 without multiplying directly.
2 2 2
19. If , , are all non zero and + + = 0, prove that: + + = 3
20. Find the value of so that (2 1) be the factor of 8 4 + 4 3 16 2 + 10 + .
1
21. If () = 2 4 + 3, evaluate (2) (1) + (2)
22. Factorise: 3 8 2 + 17 10
23. Factorise: 8( + )3 + 27( )3
24. Let 1 and 2 are the remainder when a polynomial 3 + 2 2 5 7 and
3 + 2 12 + 6 are divided by ( + 1) and ( 2) respectively. If 21 2=10,
find the value of .
25. If the polynomial () = 4 2 3 + 3 2 + 8 is divided by ( 2) leaves the
remainder 10, then find the value of .
26. Factorise: 3 3 2 10 + 24
1
27. Verify that: 3 + 3 + 3 3 = ( + + )[( )2 + ( )2 + ( )2 ]
2
28. Find the value of if the polynomial () = 4 2 3 + 3 2 + 3 7 when
divided by ( + 1) leaves the remainder 19. Also find the remainder when () is
divided by ( + 2).
29. The polynomials 3 + 32 3 and 23 5 + when divided by
4 leave the remainders 1 and 2 respectively, find the value of if 21 2 = 0.
3 3 3
30. If + + = 6 and + + = 11, find the value of + + 3.
user
The text passage is a list of mathematical problems, primarily focused on polynomials, identities, and factorization. Each problem is a distinct question, and no answers are provided within the text.

TYPE: MULTIPLE_QUESTIONS