text: 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.