Factorization, Highest Common Factor, Least Common Multiple and Square Root


1. ac +bc + ad + bd = (a+b)( __________ ).




2. x2 - 81 = (x+9) ( _______ ).



3. x2y2-y2 = y2(x+1) ( ________ ).



4. 4x2-5xy+y2 = (4x-y) ( ___________ )



5. x2-3x+2 = ( _____________ ) (x-1).



6. x3 + 8 = (x+2) ( ___________ ).



7. 1-27a3/ b3 = ( ___________ ) (1+3a/ b +9a2/b2)



8. x3+ y3 +1/x3-3y = ( _____________ ) (x2+y2 +1/x2-xy-y/x-1)



9. HCF of (x+2y) and (x2 _ 4y2) is ______________.



10. HCF of x2+3x+2 and x2+4x+3 is ______________.



11. HCF of (x2-9), (x+3)2 is ________________.



12. LCM of (x+y) and x2-y2 is _____________.



13. LCM of x2-x-2 and x2-3x+2 is _______________.



14. Simplified form of 1/x-1 + 1/x+1 = ________________.



15. Simplified form of [(x-y) (x2+xy+y2)] � (x3-y3) is ___________.



16. Square root of x2+18x+81 is _________________.



17. Square root of 64x4y2 is ____________________.



18. Simplified form of (a2+5a-14) x 1/a-2 is



19. If (x-1) is a factor of (x3-7x+m) then m = ______________.



20. LCM = product of ______________ x produced of non-common factors.



21. We can find HCF by two methods, by_____________ and division.



22. The square root of an algebraic expression consists of two expressions, which are __________ of each other.



23. According to _____________ theorem, if we get R(x)=0 (remainder is zero), on dividing a polynomial P(x) by x-a then x-a is a factor of the polynomial P(x).



24. By factorization we can find the square root of such expressions, which can be expressed as a ______________.



25. If A, B,C and D are algebraic expressions then A/B � C/D =____ where D¹ 0 , B¹ 0 and C¹ 0.



26. a4 + a4 = a8


27. (x4-y4) � (x2-y2) = x2 + y2


28. a x a x a = 3a


29. x3 + y3+z3 - 3xyz = 1/2 (x+y+z) [(x-y)2 + (y-2)2 + (z-x)2]


30. (x+1) is a factor of x3-7x-6.


31. 23 � 22 = 2


32. HCF of Z2-4 and Z+2 is (z+2).


33. x-y/x+y � (x+y)/x-y = 1


34. xy2z3/x3y2z = xyz


35. (a+b+c)3 = (a+b+c) (a+b+c)2


36. Factorization of x3+64 is (x+4) (x2+4x+16)


37. x4+x2+1 can also be written as (x2-x+1) (x2+x+1)


38. If D(x) = x-a then P(x) = (x-a) Qx+Rx as a remainder that is called remainder theorem.


39. HCF is affected by multiplying or dividing the polynomials with any number during the process of finding HCF.


40. By highest common factor two or more than two polynomials, we mean, a highest polynomial that divides completely these polynomials.


41. If H+L =A+B then H3+L3 = A3+B3 where �H� & �L� is stands for HCF and LCM respectively and A,B represents two polynomials.


42. LCM of two or more than two polynomials is a highest degree polynomial which divides completely these polynomials.


43. The relation between LCM and HCF which are represented by �L� and �H� respectively is written by AxB = HxL where �A� & �B� are two algebraic expressions.


44. LCM fo 15x2, 45xy and 30 zyx is 80x2yz.


45. The square root of a2+2ab+2ac+2bc+b2+c2 is + - (a+b+c).


46. (x+1) is not a factor of x3-7x-6


47. (x+4) (x+2) = x2+5x+4


48. 1/2 (2a2+2b2+2b2+2c2) = a2+b2+c2


49. x4+3x3-12x2-20x+48 is exactly divisible by x3+5x2-2x-24


50. (a-b) (a2+ab+b2) x a2 + b2 = (a+b)
(a2+b2) (a-b) (a+b) (a2+ab+b2)

51. Factors of x4+64 are ___________.




52. (x2-x+1) (x2+x+1) = _________.




53. To factorize algebraic expressions of the form ax2+bx+c, we find two factors p & q such that p+q=b and ___________.





54. Factorization of 4x2+8x+3 is ______________.




55. If a+b+c =0 then a3+b3+c3 =_____________.




56. (x+2y+z) (x2+4y2+z2-2xy-2yz-xz) = _____________.





57. For what value of q, x2+16x+q is a complete square = _______________.




58. HCF of 16a2b3 and 48a3b4 is _______________.




59. HCF of l2-m2 and l4-m4 is _______________.




60. LCM of z2 x5and 4x4z5 is _____________.





61. LCM of (x3-8) and (x2+2x+4) is ______________.




62. LCM of (a+4) and a3+64 is _____________.




63. A and B are two polynomials, A = x2-1, H=x-1, L=x2-1 then B= __________.




64. Simplified form of a2+b2-2ab/a2-b2 is




65. Simplified form of (x-y)/x(x+y) � x2-y2/x






66. Simplified form of (1+x/1-x ) is ______________.



67. Square root of a2+4ac+4c2 is _____________.




68. Square root of y4+ 1/ y4 +2 is _______________.




69. What will be added in 49x2+14y to make it a complete square?




70. Ö9x2-12xy+4y2 = ___________________




71. For what value of b, x2+bx+25 is a perfect square, b= ______________.





72. Square root of an algebraic expression can be calculated by ________ methods.




73. The square root of x2+8x+16 consists of two expressions, one is (x+4) and other is _____.




74. Simplified form of a3-b3/(a-b)2 is ______________.





75. Simplified form of (1-2ab)/a2+b2 is ___________.





76. x2 + 3x + 2




77. x2 + 12x +36




78. x4 � 9x2




79. x3 + 8




80. x2 � x � 6




81. a2 +ab, a2 � b2




82. (a-b) 3, (a-b) 2




83. x2-5x+6, x-2




84. (x3-8), x2-10x+16




85. x2-4, x2-5x+6




86. x2y3, x5y2




87. (x2-49) , x2-4x-21




88. 5x2y2, 20 x4 y2




89. a-b, a2-b2, (a-b) 3




90. 1-x2, 1+x3




91. x2 + 1/ x2 +2




92. 9x2+12x+4




93. x2+4xy+4y2




94. x4+ 1/ x4 +2




95. 9x2+12xy+4y2




96. x2 + 3x + 2




97. x2 + 12x +36




98. x4 � 9x2




99. x3 + 8




100. x2 � x � 6




101. a2 +ab, a2 � b2




102. (a-b) 3, (a-b) 2




103. x2-5x+6, x-2




104. (x3-8), x2-10x+16




105. x2-4, x2-5x+6




106. x2y3, x5y2




107. (x2-49) , x2-4x-21




108. 5x2y2, 20 x4 y2




109. a-b, a2-b2, (a-b) 3




110. 1-x2, 1+x3




111. x2 + 1/ x2 +2




112. 9x2+12x+4




113. x2+4xy+4y2




114. x4+ 1/ x4 +2




115. 9x2+12xy+4y2







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