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Factorization MCQs — Mathematics (page 5)

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.

101. The total cost of x items at Rs. (x + 5) each is (x^2 + 5x). If the total is Rs. 150, then x =

  1. 15
  2. 30
  3. 5
  4. 10

Answer: D) 10

Explanation: x^2 + 5x - 150 = 0 Rightarrow (x + 15)(x - 10) = 0; the number of items must be positive, so x = 10. SLO M-09-A-21 · Application

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102. Find the HCF of 12a^3b^2 and 18a^2b^4.

  1. 36a^2b^2
  2. 6a^2b^2
  3. 6a^3b^4
  4. 36a^3b^4

Answer: B) 6a^2b^2

Explanation: HCF: the HCF of the numbers (6) and the lowest power of each variable: 6a^2b^2. SLO M-09-A-19 · Understanding

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103. Find the LCM of x^2-3x-10 and x^2+6x+8.

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

Answer: D) (x+2)(x-5)(x+4)

Explanation: Take each factor the greatest number of times it appears: (x+2)(x-5)(x+4). SLO M-09-A-19 · Understanding

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104. Factorise 6x^3y^2 + 18x^2y^3.

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

Answer: A) 6x^2y^2(x + 3y)

Explanation: The HCF of the terms is 6x^2y^2; dividing each term by it leaves x + 3y. SLO M-09-A-17 · Knowledge

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105. A circular path lies between circles of radii 15 m and 13 m. Its area pi R^2 - pi r^2 equals:

  1. 4pi m²
  2. 212pi m²
  3. 59pi m²
  4. 56pi m²

Answer: D) 56pi m²

Explanation: pi(R^2 - r^2) = pi(R + r)(R - r) = pi(28)(2) = 56pi m². SLO M-09-A-21 · Application

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106. Using a^2 - b^2 = (a + b)(a - b), evaluate 75^2 - 25^2.

  1. 5,200
  2. 5,600
  3. 2,500
  4. 5,000

Answer: D) 5,000

Explanation: 75^2 - 25^2 = (100)(50) = 5000. SLO M-09-A-21 · Application

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107. Factorise by grouping: x^2 + 3x + 2x + 6

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

Answer: B) (x + 3)(x + 2)

Explanation: Group in pairs and take out common factors: x^2 + 3x + 2x + 6 = (x + 3)(x + 2). SLO M-09-A-17 · Knowledge

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108. Find the square root of 4x^2 + 9y^2 + 16 + 12xy + 16x + 24y.

  1. pm(2x - 3y + 4)
  2. pm(2x + 3y + 4)
  3. pm(2x + 3y - 4)
  4. pm(4x + 9y + 16)

Answer: B) pm(2x + 3y + 4)

Explanation: Expanding (2x + 3y + 4)^2 gives 4x^2 + 9y^2 + 16 + 12xy + 16x + 24y, so its square root is pm(2x + 3y + 4). SLO M-09-A-20 · Understanding

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109. Factorise 3x^2+10x-8.

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

Answer: B) (3x-2)(x+4)

Explanation: Split the middle term using two numbers with product 3 (-8) = -24 and sum 10; this gives 3x^2+10x-8 = (3x-2)(x+4). SLO M-09-A-18 · Understanding

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110. Evaluate 41 39 quickly.

  1. 1,599
  2. 1,601
  3. 1,600
  4. 1,589

Answer: A) 1,599

Explanation: 41 39 = (40 + 1)(40 - 1) = 40^2 - 1^2 = 1600 - 1 = 1599. SLO M-09-A-21 · Application

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111. Find the LCM of x^2+3x+2 and x^2+4x+3.

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

Answer: B) (x+1)(x+2)(x+3)

Explanation: Take each factor the greatest number of times it appears: (x+1)(x+2)(x+3). SLO M-09-A-19 · Understanding

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112. Factorise (x + 1)(x + 2)(x + 3)(x + 4) + 1.

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

Answer: A) (x^2 + 5x + 5)^2

Explanation: With y = x^2 + 5x: (y + 4)(y + 6) + 1 = y^2 + 10y + 25 = (y + 5)^2. SLO M-09-A-18 · Understanding

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113. Factorise 14x^2y - 7xy^2.

  1. 7(2x - y)
  2. 7xy(2x - y)
  3. 7xy(2x + y)
  4. 7x^2y(2x - y)

Answer: B) 7xy(2x - y)

Explanation: The HCF of the terms is 7xy; dividing each term by it leaves 2x - y. SLO M-09-A-17 · Knowledge

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114. Find the HCF of x^2-36 and x^2+7x+6.

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

Answer: A) x+6

Explanation: x^2-36 = (x+6)(x-6) and x^2+7x+6 = (x+6)(x+1). The common factor is x+6. SLO M-09-A-19 · Understanding

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