51. What must be added to x^2 + 10x to make it a perfect square?
- 50
- 25
- 10
- 20
Answer: B) 25
Explanation: Add ( 102 )^2 = 25: x^2 + 10x + 25 = (x + 5)^2. SLO M-09-A-20 · Understanding
MCQs / Mathematics / Factorization
Factorization MCQs — Mathematics (page 3)
114 multiple-choice questions on Factorization from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
52. Factorise x^2 - 9.
- (x - 3)^2
- (x + 9)(x - 1)
- (x + 3)^2
- (x + 3)(x - 3)
Answer: D) (x + 3)(x - 3)
Explanation: Difference of squares: x^2 - 3^2 = (x + 3)(x - 3). SLO M-09-A-17 · Knowledge
53. What must be added to x^2 + 14x to make it a perfect square?
- 98
- 14
- 49
- 28
Answer: C) 49
Explanation: Add ( 142 )^2 = 49: x^2 + 14x + 49 = (x + 7)^2. SLO M-09-A-20 · Understanding
54. For which values of k is x^2 + kx + 16 a perfect square?
- k = pm 10
- k = pm 4
- k = pm 8
- k = 16
Answer: C) k = pm 8
Explanation: (x pm 4)^2 = x^2 pm 8x + 16, so k = pm 8. SLO M-09-A-20 · Understanding
55. Factorise x^2-11x+18.
- (x+2)(x-9)
- (x+2)(x+9)
- (x-2)(x-9)
- (x-2)(x+9)
Answer: C) (x-2)(x-9)
Explanation: Find two numbers with product 18 and sum -11: -2 and -9. So x^2-11x+18 = (x-2)(x-9). SLO M-09-A-18 · Understanding
56. Find the HCF of x^2+6x+5 and x^2-25.
- x-5
- x+5
- x+1
- (x+5)(x+1)
Answer: B) x+5
Explanation: x^2+6x+5 = (x+5)(x+1) and x^2-25 = (x+5)(x-5). The common factor is x+5. SLO M-09-A-19 · Understanding
57. Using a^2 - b^2 = (a + b)(a - b), evaluate 1001^2 - 999^2.
- 1,001,002
- 4,000
- 4,200
- 4
Answer: B) 4,000
Explanation: 1001^2 - 999^2 = (2000)(2) = 4000. SLO M-09-A-21 · Application
58. Evaluate 53 47 quickly.
- 2,509
- 2,481
- 2,500
- 2,491
Answer: D) 2,491
Explanation: 53 47 = (50 + 3)(50 - 3) = 50^2 - 3^2 = 2500 - 9 = 2491. SLO M-09-A-21 · Application
59. By factorisation, (x^2 - 4)(x^2 + 4x + 4)(x - 2), for x 2, equals:
- (x + 2) x - 2
- (x + 2)(x - 2) x + 2
- (x - 2) x + 2
- (x + 2)^2(x - 2)
Answer: B) (x + 2)(x - 2) x + 2
Explanation: The product is (x - 2)^2(x + 2)^3; its square root is (x - 2)(x + 2) x + 2. SLO M-09-A-20 · Understanding
60. Find the square root of x^29 - 23 + 1x^2.
- pm ( x3 - 1 )
- pm ( x3 + 1x )
- pm ( x3 - 1x )
- pm ( x9 - 1x )
Answer: C) pm ( x3 - 1x )
Explanation: Expanding ( x3 - 1x )^2 gives x^29 - 23 + 1x^2, so its square root is pm ( x3 - 1x ). SLO M-09-A-20 · Understanding
61. The distance formula s = ut + 12at^2 can be factorised as:
- s = t (u + 12at )
- s = at(u + t)
- s = u (t + 12at )
- s = 12t(u + at)
Answer: A) s = t (u + 12at )
Explanation: Take out the common factor t. SLO M-09-A-21 · Application
62. The HCF of p(x) = x^2+3x+2 and q(x) = x^2+6x+5 is x+1. Using LCM = p(x) q(x) HCF, the LCM is:
- (x+1)(x+2)
- (x+2)(x+5)
- (x+1)^2(x+2)(x+5)
- (x+1)(x+2)(x+5)
Answer: D) (x+1)(x+2)(x+5)
Explanation: (x+1)(x+2) (x+1)(x+5)x+1 = (x+1)(x+2)(x+5). SLO M-09-A-19 · Understanding
63. Factorise 5x^2-13x-6.
- (5x-2)(x-3)
- (5x-3)(x+2)
- (5x-2)(x+3)
- (5x+2)(x-3)
Answer: D) (5x+2)(x-3)
Explanation: Split the middle term using two numbers with product 5 (-6) = -30 and sum -13; this gives 5x^2-13x-6 = (5x+2)(x-3). SLO M-09-A-18 · Understanding
64. Find the square root of x^2 + 2 + 1x^2.
- pm (x^2 + 1x^2 )
- pm (x - 1x )
- pm (x + 1 )
- pm (x + 1x )
Answer: D) pm (x + 1x )
Explanation: Expanding (x + 1x )^2 gives x^2 + 2 + 1x^2, so its square root is pm (x + 1x ). SLO M-09-A-20 · Understanding
65. Find the HCF of x^2-3x-10 and x^2+6x+8.
- x+2
- x+4
- x-2
- x-5
Answer: A) x+2
Explanation: x^2-3x-10 = (x+2)(x-5) and x^2+6x+8 = (x+2)(x+4). The common factor is x+2. SLO M-09-A-19 · Understanding
66. What must be added to x^2 + 6x to make it a perfect square?
- 9
- 18
- 6
- 12
Answer: A) 9
Explanation: Add ( 62 )^2 = 9: x^2 + 6x + 9 = (x + 3)^2. SLO M-09-A-20 · Understanding
67. Find the square root of x^2 + 4y^2 + 9z^2 - 4xy + 6xz - 12yz.
- pm(x + 2y + 3z)
- pm(x + 2y - 3z)
- pm(x - 2y - 3z)
- pm(x - 2y + 3z)
Answer: D) pm(x - 2y + 3z)
Explanation: Expanding (x - 2y + 3z)^2 gives x^2 + 4y^2 + 9z^2 - 4xy + 6xz - 12yz, so its square root is pm(x - 2y + 3z). SLO M-09-A-20 · Understanding
68. Algebra tiles: an x^2 tile, four x tiles and four unit tiles make a square of side:
- 2x + 2
- x + 2
- x + 1
- x + 4
Answer: B) x + 2
Explanation: x^2 + 4x + 4 = (x + 2)^2. SLO M-09-A-17 · Knowledge
69. Using a^2 - b^2 = (a + b)(a - b), evaluate 99^2 - 1^2.
- 10,000
- 10,800
- 9,604
- 9,800
Answer: D) 9,800
Explanation: 99^2 - 1^2 = (100)(98) = 9800. SLO M-09-A-21 · Application
70. Find the square root of 4x^2+12x+9.
- pm(2x-3)
- pm(4x+9)
- pm(2x+3)
- pm(2x+6)
Answer: C) pm(2x+3)
Explanation: 4x^2+12x+9 = (2x+3)^2, so the square root is pm(2x+3). SLO M-09-A-20 · Understanding
71. Find the LCM of 12a^3b^2 and 18a^2b^4.
- 6a^2b^2
- 36a^3b^4
- 36a^2b^2
- 216a^3b^4
Answer: B) 36a^3b^4
Explanation: LCM: the LCM of the numbers (36) and the highest power of each variable: 36a^3b^4. SLO M-09-A-19 · Understanding
72. Find the square root of x^4 + 6x^3 + 11x^2 + 6x + 1.
- pm(x^2 + 3x + 1)
- pm(x^2 + 3x - 1)
- pm(x^2 + 1)
- pm(x^2 + 6x + 1)
Answer: A) pm(x^2 + 3x + 1)
Explanation: Expanding (x^2 + 3x + 1)^2 gives x^4 + 6x^3 + 11x^2 + 6x + 1, so its square root is pm(x^2 + 3x + 1). SLO M-09-A-20 · Understanding
73. For which values of k is x^2 + kx + 49 a perfect square?
- k = 49
- k = pm 7
- k = pm 14
- k = pm 16
Answer: C) k = pm 14
Explanation: (x pm 7)^2 = x^2 pm 14x + 49, so k = pm 14. SLO M-09-A-20 · Understanding
74. Factorise 6x^2y + 9xy^2.
- 3xy(2x - 3y)
- 3x^2y(2x + 3y)
- 3(2x + 3y)
- 3xy(2x + 3y)
Answer: D) 3xy(2x + 3y)
Explanation: The HCF of the terms is 3xy; dividing each term by it leaves 2x + 3y. SLO M-09-A-17 · Knowledge
75. Find the HCF of 8ab^3 and 20a^4b.
- 4a^4b^3
- 4ab
- 40ab
- 40a^4b^3
Answer: B) 4ab
Explanation: HCF: the HCF of the numbers (4) and the lowest power of each variable: 4ab. SLO M-09-A-19 · Understanding