Practice sheet Class Xth (Chapter 2 H.C.F and L.C.M))


 

Practice Sheet for Chapter 2 ( H.C.F and L.C.M)

USEFUL FORMULAE

1. (x + y)2 = x2 + 2xy + y2
2. (x – y) 2 = x2 – 2xy + y2
3. (x + y + z) 2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
4. (x + y) 3 = x3 + 3x2y + 3xy2 + y3
5. (x – y) 3 = x3 – 3x2y + 3xy2 – y3
6. x2 – y2 = (x + y) (x – y)
7. x3 + y3 = (x + y) (x2 – xy + y2)
8. x3 – y3 = (x – y) (x2 + xy + y2)
9. x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
10. x4 – y4 = (x2 + y2) (x2 – y2) = (x2 + y2) (x + y) (x – y)

Find the HCF and LCM of the following pairs of polynomials: hyTW id`qIAW bhupdW dw m.s.v Aqy l.s.v pqw kro [
  1. (x + 2)2 (x – 3) and (x + 2) (x – 3)2
  2. (x + 3)2 (x – 2)
  3. x2(x + 1) (x – 3) and x(x + 1)2 (x + 2)
  4. 2x2(x + 5) and 4x3 (x + 5)2 (x + 10)
  5. 10(x2 – 1) 2 and 15(x + 1) 4 (2x + 3)
  6. 16(x2 – 1)(x2 + 1) and 24(x4 – 1)(x + 1)
  7. 3x2 + 5x – 2 and 3x2 – 7x + 2.
  8. 3 (x2 – 7x + 12) and 24 (x2 – 9x + 20).
  9. 20x2 y (x2 – y2) and 35xy2 (x – y)
  10.  8 (x3 – x2 + x) and 28 (x3 + 1).
  11. 2x3 + x2 – 3x and x3 – x.
  12.  24(4x2 – 9) and 18 (2x2 + 5x – 12)
  13. 2x2 – x – 1 and 4x2 + 8x + 3.
  14. 3x2 + 5x – 2 and 3x2 – 7x + 2.
  15. 20x2 y (x2 – y2) and 35xy2 (x – y).
  16. 42 (2x3 – 5x2 – 3x)  and 60 (8x4 + x)
  17.  6(x + 1) (x + 2)  and   9(x3 + 1)
  18. 42(x3 – 1)  and  14(x2 – 1)
  19. 11x3(x + 1) 3 and 121x(2x2 + 3x + 1)
  20. 4x3 (x3 + 27) and  10x5(x2 + 6x + 9)
  21. 5( x + 3)( x – 1 ) and 10x ( x2 -9 )( x2 - 5x + 4) are  HCF and LCM two polynomials respectively, if  2x(x-3)(x – 1) is one of the polynomial find the other polynomial.
do bhupdW dw m.s.v Aqy l.s.v kRmvwr 5( x + 3)( x – 1 ) Aqy  10x ( x2 -9 )( x2 - 5x + 4)  jykr auhnW iv`coN ie`k 2x(x-3)(x – 1) hovy qW dUsrI pqw kro [ 

 

 
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