Factorisation

Factorisation

43. The representation of an expression as the product of its factors is called

• (A) Commutativity
• (B) Distributivity
• (C) Factorisation
• (D) Expansion

42. The irreducible factorisation of 3a³ + 6a is

• (A) 3a(a² + 2)
• (B) 3(a³ + 2)
• (C) a(3a² + 6)
• (D) 3 × a × a × a + 2 × 3 × a

41. Common factor of x²y and –xy² is xy.

• (A) xy
• (B) x only
• (C) y only
• (D) None of these

40. Common factor of ax² + bx is

• (A) ax²
• (B) x²
• (C) x
• (D) bx

39. What is the value of (3x + 3x²) ÷ 3x?

• (A) 3x
• (B) 3x²
• (C) 3
• (D) 3x³

38. Which of the following is the correct value of 6x³ ÷ 3x²?

• (A) 2x²
• (B) 2x
• (C) 3x
• (D) 2x⁵

37. The common factor of 3ab and 2cd is

• (A) 1
• (B) – 1
• (C) a
• (D) c

36. An irreducible factor of 24x²y² is

• (A) x²
• (B) y²
• (C) x
• (D) 24x

35. Number of factors of (a + b)² is

• (A) 4
• (B) 3
• (C) 2
• (D) 1

34. The factorised form of 3x – 24 is

• (A) 3x × 24
• (B) 3(x – 8)
• (C) 24(x – 3)
• (D) 3(x – 12)

33. The factorisation of 2x + 4y is

• (A) 2(x + y)
• (B) 2(x + 2y)
• (C) x(2 + y)
• (D) x(x + 2y)

32. Common factor of 17abc, 34ab², 51a²b is

• (A) 17abc
• (B) 17ab
• (C) 17ac
• (D) 17a²b²c

31. Factorised form of r² – 10r + 21 is

• (A) (r – 1) (r – 4)
• (B) (r – 7) (r – 3)
• (C) (r – 7) (r + 3)
• (D) (r + 7) (r + 3)

30. Factorised form of p² – 17p – 38 is

• (A) (p – 19) (p + 2)
• (B) (p – 19) (p – 2)
• (C) (p + 19) (p + 2)
• (D) (p + 19) (p – 2)

29. On dividing 57p²qr by 114pq, we get

• (A) ¼pr
• (B) ¾pr
• (C) ½pr
• (D) 2pr

28. The factors of x² – 4 are

• (A) (x – 2), (x – 2)
• (B) (x + 2), (x – 2)
• (C) (x + 2), (x + 2)
• (D) (x – 4), (x – 4)

27. Which of the following is not the correct value of –20x⁴ ÷ 10x²?

• (A) –x² – x²
• (B) –2x²
• (C) –2x × x
• (D) –2x

26. Which of the following is the correct value of (2x)²?

• (A) 2x²
• (B) 4x²
• (C) 4x
• (D) x²

25. Factorisation of 5z² – 80 is

• (A) 5(z² – 16)
• (B) 5(z – 16)
• (C) 5(z – 4)(z + 4)
• (D) (z – 4)(z + 4)

24. The value of (–27x²y) ÷ (–9xy) is

• (A) 3xy
• (B) –3xy
• (C) –3x
• (D) 3x

23. The value of (2x² + 4) ÷ 2 is

• (A) 2x² + 2
• (B) x² + 2
• (C) x² + 4
• (D) 2x² + 4

22. Which of the following is the correct value of 3(x – 4)?

• (A) 3x – 4
• (B) 3x – 12
• (C) x – 4
• (D) x – 12

21. Which of the following is the correct value of (x + 8)²?

• (A) x² + 64
• (B) x² + x + 64
• (C) x² + 16x
• (D) x² + 16x + 64

20. Which of the following is the correct value of (x – 5)²?

• (A) x² – 25
• (B) x² – x + 25
• (C) x² – 10x + 25
• (D) x² – 10x + 5

19. Which of the following is the correct value of 2x + 3y?

• (A) 6xy
• (B) 5x + y
• (C) 2x + 3y
• (D) 5xy

18. Factorised form of 18mn + 10mnp is

• (A) 18m(n + np)
• (B) 2mn(9 + 5p)
• (C) 2mn(9 + 10p)  
• (D) 10mn(1 + p)

17. Factorised form of 4y² – 12y + 9 is

• (A) (2y – 3)(2y + 3)
• (B) (2y – 3)(2y – 3)
• (C) (y – 3)(2y – 3)  
• (D) (y – 3)(y – 3)

16. 38x³y²z ÷ 19xy² is equal to

• (A) 2x²z
• (B) 2xyz
• (C) 2x²y
• (D) 2xy

15. Simplified value of (9x – 81) ÷ 9 is

• (A) x – 9
• (B) x – 81
• (C) x + 81
• (D) x + 9

14. Factorisation of –3a² + 3ab + 3ac is

• (A) 3a (–a – b – c)
• (B) 3a (–a + b – c)
• (C) 3a (–a – b + c)
• (D) 3a (–a + b + c)

13. Irreducible factor form of the expression 10x(x + 2) (y + 3) is

• (A) 10x(x + 2) × (y + 3)
• (B) 2 × 5 × (x² + 2x) × (y + 3)
• (C) 10 × x × (x + 2) × (y + 3)
• (D) 2 × 5 × (x + 2) × (xy + 3x)

12. On dividing p(4p² – 16) by 4p(p – 2), we get

• (A) 2p + 4
• (B) 2p – 4
• (C) p + 2
• (D) p – 2

11. The value of (a + 1) (a – 1) (a² + 1) is

• (A) a³ – 1
• (B) a⁴ – 1
• (C) a⁴ + 1
• (D) a³ + 1

10. Factorised form of 23xy – 46x + 54y – 108 is

• (A) (23x + 54) (y – 2)
• (B) (23x + 54y) (y – 2)
• (C) (23xy + 54y) (–46x – 108)
• (D) (23x + 54) (y + 2)

9. Factorisation of 12a²b + 15ab² is

• (A) ab (4a + 5b)
• (B) 3ab (4a + 5b)
• (C) 3ab (4a + b)
• (D) ab (4a + 5b)

8. In the factorisation of m⁴ – 256, how many factors will be there?

• (A) 1
• (B) 2
• (C) 3
• (D) 4

7. Which of the following is the correct value of (5x² + 20x) ÷ (x + 4)?

• (A) 5
• (B) 5x
• (C) 4x
• (D) 4x(x + 4)

6. The value of (3x³ +9x² + 27x) ÷ 3x is

• (A) x² + 9 + 27x
• (B) 3x³ + 3x² + 27x
• (C) 3x³ + 9x² + 9
• (D) x² + 3x + 9

5. Simplified value of (x³ + 2x² + 3x) ÷ 2x is

• (A) x² + x² + 3
• (B) (x² + 2x + 3)/2
• (C) (x³ + 2x² + 3)/2
• (D) (x³ + 2 + 3x)/2

4. Simplified value of (3y⁸ – 4y⁶ + 5y⁴) ÷ y⁴ is

• (A) 3y⁴ – 4y² + 5
• (B) 3y⁸ – 4y⁶ + 5
• (C) 3y⁸ – 4y² + 5y⁴
• (D) 3y⁸ – 4y⁶ + 4y⁴

3. Simplified value of (p³q⁶ – p⁶q³) ÷ p³q³ is

• (A) p³q³
• (B) q⁶ – p³
• (C) q³ – p³
• (D) q³ – p⁶q³

2. Substituting x = – 3 in x² + 5x + 4 gives

• (A) (–3)² + 5(–3) + 4 = 9 + 2 + 4 = 15
• (B) (–3)² + 5(–3) + 4 = –6 + 2 + 4 = 0
• (C) (–3)² + 5(–3) + 4 = 9 – 15 + 4 = –2
• (D) (–3)² + 5(–3) + 4 = –6 – 15 + 4 = –17

1. Substituting x = – 3 in x² – 5x + 4 gives

• (A) (–3)² – 5(–3) + 4 = 9 – 8 + 4 = 5
• (B) (–3)² – 5(–3) + 4 = –6 – 8 + 4 = 10
• (C) (–3)² – 5(–3) + 4 = 9 + 15 + 4 = 28
• (D) (–3)² – 5(–3) + 4 = –6 + 15 + 4 = 13