MCQs / Mathematics / Factorization

Factorization MCQs — Mathematics (page 4)

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.

76. To factorise x^2+9x+20 we need two numbers whose sum is 9 and product is 20. They are:

  1. 1 and 20
  2. -4 and -5
  3. 4 and 5
  4. 3 and 6

Answer: C) 4 and 5

Explanation: 4 + 5 = 9 and 4 5 = 20, so x^2+9x+20 = (x+4)(x+5). SLO M-09-A-17 · Knowledge

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77. To factorise x^2+7x+12 we need two numbers whose sum is 7 and product is 12. They are:

  1. -3 and -4
  2. 2 and 5
  3. 1 and 12
  4. 3 and 4

Answer: D) 3 and 4

Explanation: 3 + 4 = 7 and 3 4 = 12, so x^2+7x+12 = (x+3)(x+4). SLO M-09-A-17 · Knowledge

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78. A circular path lies between circles of radii 10 m and 6 m. Its area pi R^2 - pi r^2 equals:

  1. 16pi m²
  2. 94pi m²
  3. 64pi m²
  4. 8pi m²

Answer: C) 64pi m²

Explanation: pi(R^2 - r^2) = pi(R + r)(R - r) = pi(16)(4) = 64pi m². SLO M-09-A-21 · Application

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79. Find the LCM of x^2-9 and x^2+x-6.

  1. (x+3)(x-3)(x-2)
  2. (x+3)^2(x-3)(x-2)
  3. (x-3)(x-2)
  4. x+3

Answer: A) (x+3)(x-3)(x-2)

Explanation: Take each factor the greatest number of times it appears: (x+3)(x-3)(x-2). SLO M-09-A-19 · Understanding

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80. A box has volume (x^3+6x^2+5x) cm³. Its dimensions could be:

  1. x, (x+5), (x+1)
  2. x, (x-1), (x-5)
  3. x^2, (x+6), 1
  4. x, (x+1), (x+5)

Answer: D) x, (x+1), (x+5)

Explanation: x^3+6x^2+5x = x(x^2 + 6x + 5) = x(x+1)(x+5). SLO M-09-A-21 · Application

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81. Factorise 8x^3 + 27.

  1. (2x + 3)^3
  2. (2x + 3)(4x^2 - 6x + 9)
  3. (2x + 3)(4x^2 + 6x + 9)
  4. (2x - 3)(4x^2 + 6x + 9)

Answer: B) (2x + 3)(4x^2 - 6x + 9)

Explanation: a^3 + b^3 = (a + b)(a^2 - ab + b^2) with a = 2x, b = 3. SLO M-09-A-18 · Understanding

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82. Find the HCF of x^2-2x-8 and x^2-x-12.

  1. x+2
  2. x-4
  3. x+4
  4. x+3

Answer: B) x-4

Explanation: x^2-2x-8 = (x-4)(x+2) and x^2-x-12 = (x-4)(x+3). The common factor is x-4. SLO M-09-A-19 · Understanding

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83. Which expression is not a perfect square?

  1. x^2 + 6x + 9
  2. 4x^2 - 4x + 1
  3. 9x^2 + 12x + 4
  4. x^2 + 6x + 4

Answer: D) x^2 + 6x + 4

Explanation: x^2 + 6x + 9 = (x + 3)^2, 4x^2 - 4x + 1 = (2x - 1)^2, 9x^2 + 12x + 4 = (3x + 2)^2, but x^2 + 6x + 4 would need 9 as its constant. SLO M-09-A-20 · Understanding

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84. Factorise by grouping: ax + ay + bx + by

  1. (a + b)(x + y)
  2. ab(x + y)
  3. (a - b)(x - y)
  4. (a + x)(b + y)

Answer: A) (a + b)(x + y)

Explanation: Group in pairs and take out common factors: ax + ay + bx + by = (a + b)(x + y). SLO M-09-A-17 · Knowledge

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85. Factorise 12x^2y^2 + 20xy^3.

  1. 4xy^2(3x - 5y)
  2. 4(3x + 5y)
  3. 4xy^2(3x + 5y)
  4. 4x^2y^2(3x + 5y)

Answer: C) 4xy^2(3x + 5y)

Explanation: The HCF of the terms is 4xy^2; dividing each term by it leaves 3x + 5y. SLO M-09-A-17 · Knowledge

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86. The square root of (x + 1x )^2 - 4 is:

  1. pm (x - 1x )
  2. pm (x + 1x - 2 )
  3. pm(x - 2)
  4. pm (x + 1x )

Answer: A) pm (x - 1x )

Explanation: (x + 1x )^2 - 4 = x^2 - 2 + 1x^2 = (x - 1x )^2. SLO M-09-A-20 · Understanding

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87. Find the LCM of 8ab^3 and 20a^4b.

  1. 40a^4b^3
  2. 4ab
  3. 40ab
  4. 160a^4b^3

Answer: A) 40a^4b^3

Explanation: LCM: the LCM of the numbers (40) and the highest power of each variable: 40a^4b^3. SLO M-09-A-19 · Understanding

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88. The area of a rectangular field is (x^2 - 16) m² and its length is (x + 4) m. Its width is:

  1. (x + 4) m
  2. (x - 4) m
  3. (x - 2) m
  4. (x - 16) m

Answer: B) (x - 4) m

Explanation: x^2 - 16 = (x + 4)(x - 4). SLO M-09-A-21 · Application

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89. Factorise x^4 + x^2 + 1.

  1. (x^2 + x - 1)(x^2 - x - 1)
  2. (x^2 + x + 1)(x^2 - x + 1)
  3. (x^2 + 1)^2
  4. (x^2 + 1)(x^2 - 1)

Answer: B) (x^2 + x + 1)(x^2 - x + 1)

Explanation: Add and subtract x^2: x^4 + 2x^2 + 1 - x^2 = (x^2 + 1)^2 - x^2 = (x^2 + x + 1)(x^2 - x + 1). SLO M-09-A-18 · Understanding

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90. Factorise x^2+5x-6.

  1. (x+6)(x+1)
  2. (x+6)(x-1)
  3. (x-6)(x+1)
  4. (x-6)(x-1)

Answer: B) (x+6)(x-1)

Explanation: Find two numbers with product -6 and sum 5: 6 and -1. So x^2+5x-6 = (x+6)(x-1). SLO M-09-A-18 · Understanding

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91. Factorise 16x^4 + 4x^2 + 1.

  1. (4x^2 + 1)^2
  2. (4x^2 + 2x + 1)(4x^2 - 2x + 1)
  3. (4x^2 + 2x - 1)(4x^2 - 2x - 1)
  4. (8x^2 + 1)(2x^2 + 1)

Answer: B) (4x^2 + 2x + 1)(4x^2 - 2x + 1)

Explanation: 16x^4 + 8x^2 + 1 - 4x^2 = (4x^2 + 1)^2 - (2x)^2 = (4x^2 + 2x + 1)(4x^2 - 2x + 1). SLO M-09-A-18 · Understanding

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92. A rectangle is made from one x^2 tile, five x tiles and six unit tiles. Its sides are:

  1. (x + 1) and (x + 6)
  2. x and (x + 5)
  3. (x + 2) and (x + 3)
  4. (x + 5) and (x + 1)

Answer: C) (x + 2) and (x + 3)

Explanation: The tiles have total area x^2 + 5x + 6 = (x + 2)(x + 3). SLO M-09-A-17 · Knowledge

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93. Factorise x^2+8x+15.

  1. (x+3)(x+5)
  2. (x+3)(x-5)
  3. (x-3)(x+5)
  4. (x-3)(x-5)

Answer: A) (x+3)(x+5)

Explanation: Find two numbers with product 15 and sum 8: 3 and 5. So x^2+8x+15 = (x+3)(x+5). SLO M-09-A-18 · Understanding

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94. Find the square root of 9x^2 + 12xy + 4y^2.

  1. pm(3x - 2y)
  2. pm(3x + 4y)
  3. pm(3x + 2y)
  4. pm(9x + 4y)

Answer: C) pm(3x + 2y)

Explanation: 9x^2 + 12xy + 4y^2 = (3x + 2y)^2. SLO M-09-A-20 · Understanding

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95. Find the HCF of 8xy^4 and 20x^3y.

  1. 40xy
  2. 4x^3y^4
  3. 4x
  4. 4xy

Answer: D) 4xy

Explanation: Take the HCF of the numbers (4) and the lowest power of each variable: 4xy. SLO M-09-A-17 · Knowledge

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96. Find the HCF of x^2-9 and x^2+x-6.

  1. (x+3)(x-3)
  2. x-2
  3. x+3
  4. x-3

Answer: C) x+3

Explanation: x^2-9 = (x+3)(x-3) and x^2+x-6 = (x+3)(x-2). The common factor is x+3. SLO M-09-A-19 · Understanding

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97. The amount with simple profit is A = P + Prt. Factorised, this is:

  1. A = Pr(1 + t)
  2. A = P(r + t)
  3. A = (P + r)t
  4. A = P(1 + rt)

Answer: D) A = P(1 + rt)

Explanation: Take P out as a common factor. SLO M-09-A-21 · Application

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98. Which is a common factor of 3x^2 - 12 and x^2 + 2x?

  1. x + 4
  2. x + 2
  3. 3x
  4. x - 2

Answer: B) x + 2

Explanation: 3x^2 - 12 = 3(x - 2)(x + 2) and x^2 + 2x = x(x + 2); both contain x + 2. SLO M-09-A-17 · Knowledge

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99. A rectangular garden has area (x^2+5x-6) m². One side is (x-1) m. The other side is:

  1. (x+5) m
  2. (x-6) m
  3. (x+6) m
  4. (x+7) m

Answer: C) (x+6) m

Explanation: x^2+5x-6 = (x-1)(x+6), so the other side is x+6. SLO M-09-A-21 · Application

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100. Find the LCM of x^2+3x-4 and x^2-7x+6.

  1. (x-1)(x+4)(x-6)
  2. (x-1)^2(x+4)(x-6)
  3. (x+4)(x-6)
  4. x-1

Answer: A) (x-1)(x+4)(x-6)

Explanation: Take each factor the greatest number of times it appears: (x-1)(x+4)(x-6). SLO M-09-A-19 · Understanding

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