9th class Math, Chapter 4: Factorization and Algebraic Manipulation MCQs

1. The factorization of 12x + 36 is:

1. (A) 12(x + 3) ✓
2. (B) 12(3x)
3. (C) 12(3x + 1)
4. (D) x(12 + 36x)

2. The factors of 4x² − 12x + 9 are:

1. (A) (2x + 3)²
2. (B) (2x − 3)² ✓
3. (C) (2x − 3)(2x + 3)
4. (D) (2 + 3x)(2 − 3x)²

3. The HCF of a³b³ and ab² is:

1. (A) a³b³
2. (B) ab² ✓
3. (C) a⁴b⁵
4. (D) a²b

4. The LCM of 16x², 4x and 30xy is:

1. (A) 480x³y
2. (B) 240xy
3. (C) 240x²y ✓
4. (D) 120x⁴y

5. Product of LCM and HCF = ______ of two polynomials.

1. (A) sum
2. (B) difference
3. (C) product ✓
4. (D) quotient

6. The square root of x² − 6x + 9 is:

1. (A) ±(x − 3) ✓
2. (B) ±(x + 3)
3. (C) x − 3
4. (D) x + 3

7. The LCM of (a − b)² and (a − b)⁴ is:

1. (A) (a − b)²
2. (B) (a − b)³
3. (C) (a − b)⁴ ✓
4. (D) (a − b)⁶

8. The factorization of x³ + 3x² + 3x + 1 is:

1. (A) (x + 1)³ ✓
2. (B) (x − 1)³
3. (C) (x + 1)(x² + x + 1)
4. (D) (x − 1)(x² − x + 1)

9. A cubic polynomial has degree:

1. (A) 1
2. (B) 2
3. (C) 3 ✓
4. (D) 4

10. One of the factors of x³ − 27 is:

1. (A) x − 3 ✓
2. (B) x + 3
3. (C) x² − 3x + 9
4. (D) both (a) and (c)

11. Which of the following is a quadratic expression?

1. (A) x³ + 5x
2. (B) 5x + 6
3. (C) x⁴ + 1
4. (D) x² + 5x + 6 ✓

12. To factorize ax² + bx + c we find two numbers whose product is:

1. (A) ac and sum is b ✓
2. (B) ab and sum is c
3. (C) bc and sum is a
4. (D) c and sum is a

13. a⁴ + a²b² + b⁴ is factorized by adding and subtracting:

1. (A) a²b² ✓
2. (B) 2ab
3. (C) a⁴
4. (D) b⁴

14. (a + b)³ equals:

1. (A) a³ + 3ab + b³
2. (B) a³ + 2a²b + 2ab² + b³
3. (C) a³ + 3a²b + 3ab² + b³ ✓
4. (D) a³ + b³

15. (a − b)³ equals:

1. (A) a³ − 3a²b + 3ab² − b³ ✓
2. (B) a³ − b³
3. (C) a³ − 3a²b − 3ab² − b³
4. (D) a³ + 3a²b − 3ab² − b³

16. a³ + b³ equals:

1. (A) (a + b)(a² + ab + b²)
2. (B) (a − b)(a² + ab + b²)
3. (C) (a + b)³
4. (D) (a + b)(a² − ab + b²) ✓

17. a³ − b³ equals:

1. (A) (a − b)(a² − ab + b²)
2. (B) (a + b)(a² − ab + b²)
3. (C) (a − b)³
4. (D) (a − b)(a² + ab + b²) ✓

18. The HCF of two or more algebraic expressions is:

1. (A) the product of the expressions
2. (B) the sum of the expressions
3. (C) the greatest expression dividing each without remainder ✓
4. (D) the smallest expression divisible by each

19. The LCM of two algebraic expressions is:

1. (A) the greatest expression dividing each
2. (B) their difference
3. (C) their HCF
4. (D) the smallest expression divisible by each of them ✓

20. For two polynomials p(x) and q(x): LCM × HCF equals:

1. (A) p(x) + q(x)
2. (B) p(x) − q(x)
3. (C) p(x)/q(x)
4. (D) p(x) · q(x) ✓