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

 1. ac +bc + ad + bd = (a+b)( __________ ).a) b+d b) a+cc) a+dd) c+d
 2. x2 - 81 = (x+9) ( _______ ).a) x/9b) x-9c) x+9
 3. x2y2-y2 = y2(x+1) ( ________ ).a) x-1b) x+1c) x/1
 4. 4x2-5xy+y2 = (4x-y) ( ___________ )a) (x/y)b) (x-y)c) (x+y)
 5. x2-3x+2 = ( _____________ ) (x-1).a) x/2b) x+2c) x-2
 6. x3 + 8 = (x+2) ( ___________ ).a) x22x+4b) x2-2x+4c) x2-2x-4
 7. 1-27a3/ b3 = ( ___________ ) (1+3a/ b +9a2/b2) a) (1-3a/b)b) (1-3a *b)c) (1-3a+b)
 8. x3+ y3 +1/x3-3y = ( _____________ ) (x2+y2 +1/x2-xy-y/x-1)a) (x+y+1-x)b) (x-y+1/x)c) (x+y+1/x)
 9. HCF of (x+2y) and (x2 _ 4y2) is ______________.a) x+2yb) x-2yc) x/2y
 10. HCF of x2+3x+2 and x2+4x+3 is ______________.a) x-1b) x/1c) x+1
 11. HCF of (x2-9), (x+3)2 is ________________.a) x-3b) x/3c) x+3
 12. LCM of (x+y) and x2-y2 is _____________.a) x2-y2b) x2-y-2c) x-2-y2
 13. LCM of x2-x-2 and x2-3x+2 is _______________.a) (x-2)(x-1)(x-1)b) (x-2)(x-1)(x+1)c) (x+2)(x-1)(x+1)
 14. Simplified form of 1/x-1 + 1/x+1 = ________________. a) 2x / x2-1b) 2x / x-2-1c) 2x / x21
 15. Simplified form of [(x-y) (x2+xy+y2)] � (x3-y3) is ___________.a) 2b) 1c) -1
 16. Square root of x2+18x+81 is _________________.a) x/9b) x+9c) x * 9
 17. Square root of 64x4y2 is ____________________.a) 8x2yb) 8x3yc) 8x-2y
 18. Simplified form of (a2+5a-14) x 1/a-2 is a) (a/7)b) (a-7)c) (a+7)
 19. If (x-1) is a factor of (x3-7x+m) then m = ______________.a) 6b) 4c) 8
 20. LCM = product of ______________ x produced of non-common factors.a) Two factorsb) Common factorsc) Mix factors
 21. We can find HCF by two methods, by_____________ and division.a) Mix factorsb) Complete Squarec) Factorization
 22. The square root of an algebraic expression consists of two expressions, which are __________ of each other.a) Mix factorsb) Complete Squarec) Additive inverse
 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).a) Factorb) AD/BCc) Complete Square
 24. By factorization we can find the square root of such expressions, which can be expressed as a ______________.a) Complete Squareb) Mix factorsc) AD/BC
 25. If A, B,C and D are algebraic expressions then A/B � C/D =____ where D¹ 0 , B¹ 0 and C¹ 0.a) AC/BDb) AD/BCc) Mix factors
 26. a4 + a4 = a8a) Falseb) True
 27. (x4-y4) � (x2-y2) = x2 + y2a) Falseb) True
 28. a x a x a = 3aa) Falseb) True
 29. x3 + y3+z3 - 3xyz = 1/2 (x+y+z) [(x-y)2 + (y-2)2 + (z-x)2]a) Trueb) False
 30. (x+1) is a factor of x3-7x-6.a) Trueb) False
 31. 23 � 22 = 2a) Falseb) True
 32. HCF of Z2-4 and Z+2 is (z+2).a) Trueb) False
 33. x-y/x+y � (x+y)/x-y = 1 a) Trueb) False
 34. xy2z3/x3y2z = xyz a) Falseb) True
 35. (a+b+c)3 = (a+b+c) (a+b+c)2a) Falseb) True
 36. Factorization of x3+64 is (x+4) (x2+4x+16)a) Falseb) True
 37. x4+x2+1 can also be written as (x2-x+1) (x2+x+1)a) Trueb) False
 38. If D(x) = x-a then P(x) = (x-a) Qx+Rx as a remainder that is called remainder theorem.a) Trueb) False
 39. HCF is affected by multiplying or dividing the polynomials with any number during the process of finding HCF.a) Trueb) False
 40. By highest common factor two or more than two polynomials, we mean, a highest polynomial that divides completely these polynomials.a) Falseb) True
 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.a) Trueb) False
 42. LCM of two or more than two polynomials is a highest degree polynomial which divides completely these polynomials.a) Falseb) True
 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.a) Falseb) True
 44. LCM fo 15x2, 45xy and 30 zyx is 80x2yz.a) Falseb) True
 45. The square root of a2+2ab+2ac+2bc+b2+c2 is + - (a+b+c).a) Falseb) True
 46. (x+1) is not a factor of x3-7x-6a) Trueb) False
 47. (x+4) (x+2) = x2+5x+4a) Falseb) True
 48. 1/2 (2a2+2b2+2b2+2c2) = a2+b2+c2a) Falseb) True
 49. x4+3x3-12x2-20x+48 is exactly divisible by x3+5x2-2x-24a) Falseb) True
 50. (a-b) (a2+ab+b2) x a2 + b2 = (a+b) (a2+b2) (a-b) (a+b) (a2+ab+b2) a) Trueb) False
 51. Factors of x4+64 are ___________. a) (x2-4x+8)(x2+4x+8) b) (x+8) (x+4)c) (x-4) (x+4)d) (x2+4x-8) (x2+4x+8)
 52. (x2-x+1) (x2+x+1) = _________. a) x4+x2-1 b) x8+x2+1c) x4-x2+1d) (x4+x2+1)
 53. To factorize algebraic expressions of the form ax2+bx+c, we find two factors p & q such that p+q=b and ___________. a) pq =ac b) p+q =acc) p-q =acd) q=be) p=a
 54. Factorization of 4x2+8x+3 is ______________. a) (2x+3) (2x+1) b) (2x-3) (2x+1)c) (2x-3) (2x-1)d) (x+3) (x+1)
 55. If a+b+c =0 then a3+b3+c3 =_____________. a) 2abc b) 3a3b3c3c) -3abcd) 3abc
 56. (x+2y+z) (x2+4y2+z2-2xy-2yz-xz) = _____________. a) x3M-8y3+z3+6xyz b) x3+8y3-z3-6xyzc) x3+8y3+z3+6xyzd) x3+8y3+z3+12xyze) x5+8y5+z5+6xyz
 57. For what value of q, x2+16x+q is a complete square = _______________. a) -8 b) 8c) -64d) 64
 58. HCF of 16a2b3 and 48a3b4 is _______________. a) 16a2b3 b) 8abc) 48abd) 16a2b2
 59. HCF of l2-m2 and l4-m4 is _______________. a) None of these b) l-mc) l+md) l2+m2
 60. LCM of z2 x5and 4x4z5 is _____________. a) 4x5z5 b) 4xzc) 4x4z4d) x5z5e) x4z4
 61. LCM of (x3-8) and (x2+2x+4) is ______________. a) x2-2x+4 b) x3-8c) x3+8d) x2+2x+4
 62. LCM of (a+4) and a3+64 is _____________. a) a3+64 b) a2-4a+16c) a+4d) a-4
 63. A and B are two polynomials, A = x2-1, H=x-1, L=x2-1 then B= __________. a) x-1 b) x+1c) x2-1d) x2+1
 64. Simplified form of a2+b2-2ab/a2-b2 is a) a+b/a-b b) a2-b2c) a2+b2d) (a-b)/a+b
 65. Simplified form of (x-y)/x(x+y) � x2-y2/x a) x+y b) (x-y)2c) (x+y)2d) 1e) 1/(x+y)2
 66. Simplified form of (1+x/1-x ) is ______________. a) 1+x b) 1-xc) 1/1+xd) 1/1-x
 67. Square root of a2+4ac+4c2 is _____________. a) a-2c b) a2+4c2c) + - (a+2c)d) a2-4c2
 68. Square root of y4+ 1/ y4 +2 is _______________. a) + - (y2+1/y) b) + - (y-1/y)c) + - (y2 - 1/y)d) + - (y + 1/y)
 69. What will be added in 49x2+14y to make it a complete square? a) 7y2 b) 2y2c) yd) y2
 70. Ö9x2-12xy+4y2 = ___________________ a) + - (3x-2y) b) + - (3x2-2y2)c) + - (3x2+2y2)d) + - (3x+2y)
 71. For what value of b, x2+bx+25 is a perfect square, b= ______________. a) 10 b) 2c) 5xd) 10xe) 5
 72. Square root of an algebraic expression can be calculated by ________ methods. a) Division b) Division and Multiplicationc) Factorization & Divisiond) Factorization
 73. The square root of x2+8x+16 consists of two expressions, one is (x+4) and other is _____. a) - (x+4) b) + - (x-4)c) (x+4)d) + - (x+4)
 74. Simplified form of a3-b3/(a-b)2 is ______________. a) a+b/a - b b) a2+ab+b2/a-bc) a2+ab+b2/a+bd) a-b/a+b
 75. Simplified form of (1-2ab)/a2+b2 is ___________. a) (a-b)2/a-b b) (a+b)2/a+bc) (a+b)2/ a2+b2d) (a-b)2/a2+b2
 76. x2 + 3x + 2a) (x+2) (x+1) b) (x+6) 2c) (x-2) (x+3)d) (x+2) (x-3)
 77. x2 + 12x +36a) (x+6) 2 b) (x+2) (x2-2x+4)c) (x+2) (x+1)d) (x-2) (x+3)
 78. x4 � 9x2a) (x+2) (x2-2x+4) b) (x-2) (x+3)c) (x2-3x) (x2-3x)d) (x2+3x) (x2-3x)
 79. x3 + 8a) (x2-3x) (x2-3x) b) (x+6) 2c) (x+2) (x2-2x+4)d) (x2+3x) (x2-3x)
 80. x2 � x � 6a) (x-2) (x+3) b) (x+6) 2c) (x+2) (x-3)d) (x+2) (x+1)
 81. a2 +ab, a2 � b2a) a (a+b) (a-b) b) (x-2) (x+8) (x2+2x+4)c) (x-2) (x-8) (x2+2x+4)d) (x-2) (x2 +x +6)
 82. (a-b) 3, (a-b) 2a) (x-2) (x2 +x +6) b) (a-b) 3c) a (a+b) (a-b)d) (x-3) (x-2)
 83. x2-5x+6, x-2a) (x-3) (x-2) b) (a-b) 3c) a (a+b) (a-b)d) (x-2) (x-8) (x2+2x+4)
 84. (x3-8), x2-10x+16a) (x-2) (x-8) (x2+2x+4) b) a (a+b) (a-b)c) (x-2) (x2 +x +6)d) (a-b) 3
 85. x2-4, x2-5x+6a) (x-2) (x+8) (x2+2x+4) b) (x-2) (x2-x-6)c) (x-2) (x-8) (x2+2x+4)d) (x-2) (x2 +x +6)
 86. x2y3, x5y2a) a2y2 b) 5x2y2c) 5x2y4d) x2y2
 87. (x2-49) , x2-4x-21a) (1+x) b) (x-7)c) a2y2d) (a-b)
 88. 5x2y2, 20 x4 y2a) a2y2 b) 5x2y2c) 5x2y4d) x2y2
 89. a-b, a2-b2, (a-b) 3a) a2y2 b) (1+x)c) (a-b)d) (x-7)
 90. 1-x2, 1+x3a) (1-x) b) (a-b)c) (x-7)d) (1+x)
 91. x2 + 1/ x2 +2 a) +-(x+1/x) b) +- (3x +2)c) +-(3x-2y)d) +-(3x+2y)
 92. 9x2+12x+4a) +- (3x +2) b) +-(3x-2y)c) +-(3x+2y)d) +- (x+2y) 2
 93. x2+4xy+4y2a) +- (3x +2) b) +- (x+2y) 2c) +-(3x-2y)d) +-(3x+2y)
 94. x4+ 1/ x4 +2 a) +- (x2+1/x2) b) +- (x+2y) 2c) +-(x+1/x)d) +- (x+2y) 2
 95. 9x2+12xy+4y2a) +- (x+2y) 2 b) +-(3x-2y)c) +-(3x+2y)d) +-(3x +2)
 96. x2 + 3x + 2a) (x+2) (x-3) b) (x+2) (x+1)c) (x+6) 2d) (x-2) (x+3)
 97. x2 + 12x +36a) (x+2) (x+1) b) (x+2) (x2-2x+4)c) (x+6) 2d) (x-2) (x+3)
 98. x4 � 9x2a) (x+2) (x2-2x+4) b) (x-2) (x+3)c) (x2-3x) (x2-3x)d) (x2+3x) (x2-3x)
 99. x3 + 8a) (x+6) 2 b) (x+2) (x2-2x+4)c) (x2-3x) (x2-3x)d) (x2+3x) (x2-3x)
 100. x2 � x � 6a) (x+6) 2 b) (x+2) (x-3)c) (x-2) (x+3)d) (x+2) (x+1)
 101. a2 +ab, a2 � b2a) (x-2) (x2 +x +6) b) (x-2) (x+8) (x2+2x+4)c) a (a+b) (a-b)d) (x-2) (x-8) (x2+2x+4)
 102. (a-b) 3, (a-b) 2a) a (a+b) (a-b) b) (x-3) (x-2)c) (a-b) 3d) (x-2) (x2 +x +6)
 103. x2-5x+6, x-2a) a (a+b) (a-b) b) (x-3) (x-2)c) (a-b) 3d) (x-2) (x-8) (x2+2x+4)
 104. (x3-8), x2-10x+16a) (x-2) (x2 +x +6) b) (a-b) 3c) (x-2) (x-8) (x2+2x+4)d) a (a+b) (a-b)
 105. x2-4, x2-5x+6a) (x-2) (x-8) (x2+2x+4) b) (x-2) (x+8) (x2+2x+4)c) (x-2) (x2-x-6)d) (x-2) (x2 +x +6)
 106. x2y3, x5y2a) x2y2 b) a2y2c) 5x2y2d) 5x2y4
 107. (x2-49) , x2-4x-21a) a2y2 b) (1+x)c) (a-b)d) (x-7)
 108. 5x2y2, 20 x4 y2a) 5x2y2 b) 5x2y4c) a2y2d) x2y2
 109. a-b, a2-b2, (a-b) 3a) (1+x) b) (a-b)c) (x-7)d) a2y2
 110. 1-x2, 1+x3a) (x-7) b) (1+x)c) (1-x)d) (a-b)
 111. x2 + 1/ x2 +2 a) +- (3x +2) b) +-(3x+2y)c) +-(3x-2y)d) +-(x+1/x)
 112. 9x2+12x+4a) +- (3x +2) b) +-(3x-2y)c) +- (x+2y) 2d) +-(3x+2y)
 113. x2+4xy+4y2a) +- (x+2y) 2 b) +- (3x +2)c) +-(3x-2y)d) +-(3x+2y)
 114. x4+ 1/ x4 +2 a) +- (x+2y) 2 b) +- (x+2y) 2c) +-(x+1/x)d) +- (x2+1/x2)
 115. 9x2+12xy+4y2a) +-(3x-2y) b) +-(3x+2y)c) +-(3x +2)d) +- (x+2y) 2

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