Factorisation

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