MCQs / Mathematics / Factorization

Factorization MCQs — Mathematics (page 2)

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.

26. To factorise x^2+2x-15 we need two numbers whose sum is 2 and product is -15. They are:

  1. -3 and 5
  2. -4 and 6
  3. 1 and -15
  4. 3 and -5

Answer: A) -3 and 5

Explanation: -3 + 5 = 2 and -3 5 = -15, so x^2+2x-15 = (x-3)(x+5). SLO M-09-A-17 · Knowledge

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27. A rectangular garden has area (x^2+7x+10) m². One side is (x+2) m. The other side is:

  1. (x+10) m
  2. (x+5) m
  3. (x-5) m
  4. (x+7) m

Answer: B) (x+5) m

Explanation: x^2+7x+10 = (x+2)(x+5), so the other side is x+5. SLO M-09-A-21 · Application

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28. Factorise 4x^2-11x+6.

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

Answer: A) (4x-3)(x-2)

Explanation: Split the middle term using two numbers with product 4 6 = 24 and sum -11; this gives 4x^2-11x+6 = (4x-3)(x-2). SLO M-09-A-18 · Understanding

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29. Factorise 27a^3 - 125.

  1. (3a - 5)(9a^2 + 15a + 25)
  2. (3a - 5)(9a^2 - 15a + 25)
  3. (3a + 5)(9a^2 - 15a + 25)
  4. (3a - 5)(9a^2 + 25)

Answer: A) (3a - 5)(9a^2 + 15a + 25)

Explanation: a^3 - b^3 form with 3a and 5: (3a - 5) ((3a)^2 + 3a 5 + 5^2 ). SLO M-09-A-18 · Understanding

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30. Find the HCF of 14x^2y^3 and 21x^4y^2.

  1. 7x^2y^2
  2. 7x^2
  3. 42x^2y^2
  4. 7x^4y^3

Answer: A) 7x^2y^2

Explanation: Take the HCF of the numbers (7) and the lowest power of each variable: 7x^2y^2. SLO M-09-A-17 · Knowledge

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31. Factorise 2x^2+5x+3.

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

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

Explanation: Split the middle term using two numbers with product 2 3 = 6 and sum 5; this gives 2x^2+5x+3 = (2x+3)(x+1). SLO M-09-A-18 · Understanding

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32. Factorise 8x^3 - 36x^2 + 54x - 27.

  1. (2x - 3)(4x^2 + 9)
  2. (8x - 27)(x^2 + 1)
  3. (2x - 3)^3
  4. (2x + 3)^3

Answer: C) (2x - 3)^3

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

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33. To factorise x^2-x-12 we need two numbers whose sum is -1 and product is -12. They are:

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

Answer: C) -4 and 3

Explanation: -4 + 3 = -1 and -4 3 = -12, so x^2-x-12 = (x-4)(x+3). SLO M-09-A-17 · Knowledge

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34. Factorise x^3 - 64.

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

Answer: D) (x - 4)(x^2 + 4x + 16)

Explanation: a^3 - b^3 = (a - b)(a^2 + ab + b^2) with a = x, b = 4. SLO M-09-A-18 · Understanding

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35. Factorise 15x^3y - 20x^2y^2.

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

Answer: D) 5x^2y(3x - 4y)

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

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36. The HCF of p(x) = x^2+x-12 and q(x) = x^2-2x-3 is x-3. Using LCM = p(x) q(x) HCF, the LCM is:

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

Answer: A) (x-3)(x+4)(x+1)

Explanation: (x-3)(x+4) (x-3)(x+1)x-3 = (x-3)(x+4)(x+1). SLO M-09-A-19 · Understanding

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37. Factorise (x^2 + 3x + 2)(x^2 + 3x + 4) - 8.

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

Answer: C) x(x + 3)(x^2 + 3x + 6)

Explanation: Let y = x^2 + 3x: (y + 2)(y + 4) - 8 = y^2 + 6y = y(y + 6) = x(x + 3)(x^2 + 3x + 6). SLO M-09-A-18 · Understanding

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38. Factorise 4x^2-8x-5.

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

Answer: B) (2x-5)(2x+1)

Explanation: Split the middle term using two numbers with product 4 (-5) = -20 and sum -8; this gives 4x^2-8x-5 = (2x-5)(2x+1). SLO M-09-A-18 · Understanding

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39. The area of a square plot is (9x^2 + 30x + 25) m². Its side is:

  1. (x + 5) m
  2. (3x + 25) m
  3. (3x + 5) m
  4. (9x + 5) m

Answer: C) (3x + 5) m

Explanation: 9x^2 + 30x + 25 = (3x + 5)^2. SLO M-09-A-21 · Application

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40. A ball is thrown up; its height is h = 20t - 5t^2 metres. Factorise to find when it lands back on the ground.

  1. t = 4 s
  2. t = 20 s
  3. t = 5 s
  4. t = 2 s

Answer: A) t = 4 s

Explanation: h = 5t(4 - t) = 0 when t = 0 (start) or t = 4 s (landing). SLO M-09-A-21 · Application

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41. Find the square root of 9x^2-24x+16.

  1. pm(9x+16)
  2. pm(3x-4)
  3. pm(3x+4)
  4. pm(3x-8)

Answer: B) pm(3x-4)

Explanation: 9x^2-24x+16 = (3x-4)^2, so the square root is pm(3x-4). SLO M-09-A-20 · Understanding

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42. Find the HCF of 15x^3y^2 and 25x^2y^2.

  1. 75x^2y^2
  2. 5x^2y^2
  3. 5x^2
  4. 5x^3y^2

Answer: B) 5x^2y^2

Explanation: Take the HCF of the numbers (5) and the lowest power of each variable: 5x^2y^2. SLO M-09-A-17 · Knowledge

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43. Find the square root of x^2-18x+81.

  1. pm(x+81)
  2. pm(x+9)
  3. pm(x-9)
  4. pm(x-18)

Answer: C) pm(x-9)

Explanation: x^2-18x+81 = (x-9)^2, so the square root is pm(x-9). SLO M-09-A-20 · Understanding

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44. Factorise x^2+11x+24.

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

Answer: D) (x+8)(x+3)

Explanation: Find two numbers with product 24 and sum 11: 8 and 3. So x^2+11x+24 = (x+8)(x+3). SLO M-09-A-18 · Understanding

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45. Find the HCF of 9x^3y^3 and 6x^2y^5.

  1. 3x^3y^5
  2. 3x^2y^3
  3. 18x^2y^3
  4. 3x^2

Answer: B) 3x^2y^3

Explanation: Take the HCF of the numbers (3) and the lowest power of each variable: 3x^2y^3. SLO M-09-A-17 · Knowledge

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46. Find the square root of 4x^4 - 12x^3 + 25x^2 - 24x + 16.

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

Answer: D) pm(2x^2 - 3x + 4)

Explanation: Expanding (2x^2 - 3x + 4)^2 gives 4x^4 - 12x^3 + 25x^2 - 24x + 16, so its square root is pm(2x^2 - 3x + 4). SLO M-09-A-20 · Understanding

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47. Factorise 6x^2+5x-4.

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

Answer: D) (3x+4)(2x-1)

Explanation: Split the middle term using two numbers with product 6 (-4) = -24 and sum 5; this gives 6x^2+5x-4 = (3x+4)(2x-1). SLO M-09-A-18 · Understanding

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48. A stone's height is h = 30t - 5t^2 m. It is at ground level again after:

  1. 6 s
  2. 3 s
  3. 30 s
  4. 5 s

Answer: A) 6 s

Explanation: 5t(6 - t) = 0 Rightarrow t = 6 s. SLO M-09-A-21 · Application

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49. Factorise x^2+3x-28.

  1. (x+4)(x+7)
  2. (x+4)(x-7)
  3. (x-4)(x+7)
  4. (x-4)(x-7)

Answer: C) (x-4)(x+7)

Explanation: Find two numbers with product -28 and sum 3: -4 and 7. So x^2+3x-28 = (x-4)(x+7). SLO M-09-A-18 · Understanding

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50. A box has volume (x^3+6x^2+8x) cm³. Its dimensions could be:

  1. x^2, (x+6), 1
  2. x, (x+8), (x+1)
  3. x, (x-2), (x-4)
  4. x, (x+2), (x+4)

Answer: D) x, (x+2), (x+4)

Explanation: x^3+6x^2+8x = x(x^2 + 6x + 8) = x(x+2)(x+4). SLO M-09-A-21 · Application

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