MCQs / Mathematics / Factorization

Factorization MCQs — Mathematics

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.

1. Factorise 5x(a - b) + 3y(a - b).

  1. (a - b)(5x - 3y)
  2. (a + b)(5x + 3y)
  3. 15xy(a - b)
  4. (a - b)(5x + 3y)

Answer: D) (a - b)(5x + 3y)

Explanation: (a - b) is a common factor of both terms. SLO M-09-A-17 · Knowledge

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2. Find the LCM of 15a^2b^2 and 10a^3b.

  1. 30a^2b
  2. 5a^2b
  3. 150a^3b^2
  4. 30a^3b^2

Answer: D) 30a^3b^2

Explanation: LCM: the LCM of the numbers (30) and the highest power of each variable: 30a^3b^2. SLO M-09-A-19 · Understanding

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3. A rectangular garden has area (x^2+7x+12) m². One side is (x+3) m. The other side is:

  1. (x+7) m
  2. (x-4) m
  3. (x+4) m
  4. (x+12) m

Answer: C) (x+4) m

Explanation: x^2+7x+12 = (x+3)(x+4), so the other side is x+4. SLO M-09-A-21 · Application

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

  1. (x^2 + 5x + 3)(x^2 + 5x + 7)
  2. (x^2 + 5x + 4)(x^2 + 5x + 6)
  3. (x^2 + 5x + 1)(x^2 + 5x + 9)
  4. (x + 3)^2(x + 7)^2

Answer: A) (x^2 + 5x + 3)(x^2 + 5x + 7)

Explanation: Pair (x + 1)(x + 4) = y + 4 and (x + 2)(x + 3) = y + 6 with y = x^2 + 5x: (y + 4)(y + 6) - 3 = y^2 + 10y + 21 = (y + 3)(y + 7). SLO M-09-A-18 · Understanding

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5. Factorise x^4 + 64.

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

Answer: D) (x^2 + 4x + 8)(x^2 - 4x + 8)

Explanation: x^4 + 16x^2 + 64 - 16x^2 = (x^2 + 8)^2 - (4x)^2 = (x^2 + 4x + 8)(x^2 - 4x + 8). SLO M-09-A-18 · Understanding

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6. Factorise x^4 + 4.

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

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

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

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7. Find the LCM of 6a^4b and 9a^2b^3.

  1. 54a^4b^3
  2. 3a^2b
  3. 18a^4b^3
  4. 18a^2b

Answer: C) 18a^4b^3

Explanation: LCM: the LCM of the numbers (18) and the highest power of each variable: 18a^4b^3. SLO M-09-A-19 · Understanding

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8. Factorise by grouping: pq - 2p + 3q - 6

  1. (p + 2)(q - 3)
  2. (p - 2)(q + 3)
  3. (p - 3)(q + 2)
  4. (p + 3)(q - 2)

Answer: D) (p + 3)(q - 2)

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

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9. Factorise x^2+13x+36.

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

Answer: C) (x+4)(x+9)

Explanation: Find two numbers with product 36 and sum 13: 4 and 9. So x^2+13x+36 = (x+4)(x+9). SLO M-09-A-18 · Understanding

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10. Find the HCF of x^2+3x-4 and x^2-7x+6.

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

Answer: B) x-1

Explanation: x^2+3x-4 = (x-1)(x+4) and x^2-7x+6 = (x-1)(x-6). The common factor is x-1. SLO M-09-A-19 · Understanding

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11. Evaluate 102 98 quickly.

  1. 10,000
  2. 10,004
  3. 9,996
  4. 9,986

Answer: C) 9,996

Explanation: 102 98 = (100 + 2)(100 - 2) = 100^2 - 2^2 = 10000 - 4 = 9996. SLO M-09-A-21 · Application

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12. Find the square root of 36x^2+60x+25.

  1. pm(6x+10)
  2. pm(6x-5)
  3. pm(6x+5)
  4. pm(36x+25)

Answer: C) pm(6x+5)

Explanation: 36x^2+60x+25 = (6x+5)^2, so the square root is pm(6x+5). SLO M-09-A-20 · Understanding

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13. Find the HCF of 6a^4b and 9a^2b^3.

  1. 3a^4b^3
  2. 3a^2b
  3. 18a^4b^3
  4. 18a^2b

Answer: B) 3a^2b

Explanation: HCF: the HCF of the numbers (3) and the lowest power of each variable: 3a^2b. SLO M-09-A-19 · Understanding

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14. For two polynomials p(x) and q(x), which is always true?

  1. HCF = LCM
  2. HCF LCM = p(x) q(x)
  3. LCM = p(x) + q(x)
  4. HCF + LCM = p(x) + q(x)

Answer: B) HCF LCM = p(x) q(x)

Explanation: The product of two expressions equals the product of their HCF and LCM (up to a constant factor). SLO M-09-A-19 · Understanding

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15. Using a^2 - b^2 = (a + b)(a - b), evaluate 205^2 - 195^2.

  1. 4,200
  2. 41,830
  3. 4,000
  4. 100

Answer: C) 4,000

Explanation: 205^2 - 195^2 = (400)(10) = 4000. SLO M-09-A-21 · Application

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16. Find the square root of 25x^2 - 30xy + 9y^2.

  1. pm(5x - 3y)
  2. pm(25x + 9y)
  3. pm(5x + 6y)
  4. pm(5x + 3y)

Answer: A) pm(5x - 3y)

Explanation: 25x^2 - 30xy + 9y^2 = (5x - 3y)^2. SLO M-09-A-20 · Understanding

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17. Find the HCF of 15a^2b^2 and 10a^3b.

  1. 5a^3b^2
  2. 30a^2b
  3. 30a^3b^2
  4. 5a^2b

Answer: D) 5a^2b

Explanation: HCF: the HCF of the numbers (5) and the lowest power of each variable: 5a^2b. SLO M-09-A-19 · Understanding

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18. A shop's revenue is R = 40p - p^2 rupees (thousands) at price p. For which non-zero price is the revenue zero?

  1. p = 4
  2. p = 40
  3. p = 1600
  4. p = 20

Answer: B) p = 40

Explanation: R = p(40 - p) = 0 when p = 0 or p = 40. SLO M-09-A-21 · Application

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19. To factorise x^2-8x+15 we need two numbers whose sum is -8 and product is 15. They are:

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

Answer: C) -5 and -3

Explanation: -5 + (-3) = -8 and -5 (-3) = 15, so x^2-8x+15 = (x-5)(x-3). SLO M-09-A-17 · Knowledge

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20. Factorise x^2+10x-24.

  1. (x+12)(x-2)
  2. (x-12)(x-2)
  3. (x-12)(x+2)
  4. (x+12)(x+2)

Answer: A) (x+12)(x-2)

Explanation: Find two numbers with product -24 and sum 10: 12 and -2. So x^2+10x-24 = (x+12)(x-2). SLO M-09-A-18 · Understanding

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21. Find the square root of 16x^2-56x+49.

  1. pm(4x-14)
  2. pm(16x+49)
  3. pm(4x-7)
  4. pm(4x+7)

Answer: C) pm(4x-7)

Explanation: 16x^2-56x+49 = (4x-7)^2, so the square root is pm(4x-7). SLO M-09-A-20 · Understanding

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22. Find the square root of 25x^2+10x+1.

  1. pm(5x-1)
  2. pm(5x+2)
  3. pm(5x+1)
  4. pm(25x+1)

Answer: C) pm(5x+1)

Explanation: 25x^2+10x+1 = (5x+1)^2, so the square root is pm(5x+1). SLO M-09-A-20 · Understanding

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23. Factorise x^3 + 6x^2 + 12x + 8.

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

Answer: D) (x + 2)^3

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

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24. Find the HCF of 12x^2y and 18xy^3.

  1. 6x^2y^3
  2. 6x
  3. 6xy
  4. 36xy

Answer: C) 6xy

Explanation: Take the HCF of the numbers (6) and the lowest power of each variable: 6xy. SLO M-09-A-17 · Knowledge

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25. 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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