Class 9 Maths Chapter 4 – Factorization and Algebraic Manipulation-MCQs (FBISE) - MCQs

Description: Practice Class 9 Maths Chapter 4 MCQs on Factorization and Algebraic Manipulation according to the latest FBISE syllabus. These exam-oriented questions cover algebraic identities, factorization techniques, HCF, LCM, and algebraic fractions.

🔹 Go to Class 9 Maths Chapter-wise MCQs
🔹 Go to All Subjects MCQs

← Go to Chapter 3
Go to Chapter 5 →

1. The expression $a^2-b^2$ can be factorized as:

A) $(a+b)(a-b)$
B) $(a-b)^2$
C) $(a+b)^2$
D) $a(a-b)$

2. Which identity is equal to $(a+b)^2$ ?

A) $a^2+b^2$
B) $a^2-2ab+b^2$
C) $a^2+2ab+b^2$
D) $2a+2b$

3. The greatest common factor of $6x^2$ and $9x$ is:

A) $18x^2$
B) $3x$
C) $6x$
D) $9x^2$

4. Factorizing an expression means writing it as:

A) A sum of terms
B) A difference of terms
C) A quotient
D) A product of simpler factors

5. Which method should be used first when every term has a common factor?

A) Taking out the common factor
B) Completing the square
C) Long division
D) Using logarithms

6. The factorization of $x^2+5x+6$ is:

A) $(x+1)(x+6)$
B) $(x+2)(x+2)$
C) $(x+2)(x+3)$
D) $(x-2)(x-3)$

7. The HCF of two algebraic expressions is the:

A) Largest multiple
B) Greatest common factor
C) Least common factor
D) Product of all factors

8. Which identity represents the difference of squares?

A) $a^2-b^2=(a+b)(a-b)$
B) $(a+b)^2=a^2+b^2$
C) $(a-b)^2=a^2-b^2$
D) $a^2+b^2=(a+b)^2$

9. Which expression is already completely factorized?

A) $x^2-4$
B) $x^2+2x+1$
C) $2x+4$
D) $(x-3)(x+5)$

10. The LCM of algebraic expressions is the:

A) Smallest factor
B) Least common multiple
C) Greatest common divisor
D) Product of constants only

11. Which algebraic identity gives $(a-b)^2$ ?

A) $a^2+2ab+b^2$
B) $a^2-b^2$
C) $a^2-2ab+b^2$
D) $a^2+ab+b^2$

12. Simplifying algebraic fractions usually requires:

A) Factorization of numerator and denominator
B) Multiplication by zero
C) Ignoring common factors
D) Converting into decimals

13. The expression $x^2-9$ factors into:

A) $(x+9)(x-1)$
B) $(x-9)^2$
C) $(x+3)^2$
D) $(x+3)(x-3)$

14. Which concept is most useful for simplifying rational algebraic expressions?

A) Statistics
B) Factorization
C) Bearings
D) Coordinate geometry

15. The product of the HCF and LCM of two monomials equals:

A) Their sum
B) Their difference
C) The product of the two monomials
D) Their quotient

16. Which factor is common in $8x^3y$ and $12x^2y^2$ ?

A) $4x^2y$
B) $8x^3y^2$
C) $12x^2y$
D) $24x^3y^2$

17. Factorization is primarily used to:

A) Increase the degree of a polynomial
B) Convert variables into constants
C) Eliminate algebraic identities
D) Rewrite expressions in a simpler multiplicative form

18. The factorization of $x^2-16$ is:

A) $(x-4)^2$
B) $(x+4)(x-4)$
C) $(x+8)(x-2)$
D) $x(x-16)$

19. Which identity is used to factorize $a^2+2ab+b^2$ ?

A) $(a+b)^2$
B) $(a-b)^2$
C) $(a+b)(a-b)$
D) $a(a+b)$

20. The HCF of $15x^2y$ and $20xy^2$ is:

A) $5x^2y^2$
B) $10xy$
C) $15xy$
D) $5xy$

21. Which expression is a perfect square trinomial?

A) $x^2+5x+4$
B) $x^2-9$
C) $x^2+6x+9$
D) $x^2+7x+10$

22. Which factor is common to $12a^2b$ and $18ab^2$ ?

A) $6ab$
B) $12ab$
C) $3a^2b^2$
D) $18ab$

23. Before adding algebraic fractions, we should first determine the:

A) HCF
B) LCM of the denominators
C) Square root
D) Difference of the numerators

24. The factorization of $x^2-10x+25$ is:

A) $(x-25)^2$
B) $(x-10)(x-5)$
C) $(x+5)^2$
D) $(x-5)^2$

25. Which method is most appropriate for factorizing $xy+xz$ ?

A) Taking out the common factor $x$
B) Difference of squares
C) Completing the square
D) Using logarithms

26. Which polynomial has $(x-2)$ as a factor?

A) $x^2+3x+2$
B) $x^2+5x+6$
C) $x^2-5x+6$
D) $x^2+x+1$

27. The LCM of $2x$ and $3x^2$ is:

A) $6x$
B) $6x^2$
C) $3x$
D) $2x^2$

28. Which identity represents the expansion of $(a+b)(a-b)$ ?

A) $a^2+2ab+b^2$
B) $a^2-2ab+b^2$
C) $a^2+b^2$
D) $a^2-b^2$

29. Simplifying an algebraic fraction often requires cancellation of:

A) Common factors
B) Common terms only
C) Variables only
D) Coefficients only

30. The expression $x^2+7x+12$ factors into:

A) $(x+2)(x+5)$
B) $(x+1)(x+12)$
C) $(x+3)(x+4)$
D) $(x-3)(x-4)$

31. If the HCF of two expressions is 1, they are called:

A) Equal expressions
B) Relatively prime expressions
C) Perfect squares
D) Polynomial identities

32. The factorization of $4x^2-25$ is:

A) $(2x-25)(2x+1)$
B) $(4x-5)(x+5)$
C) $(2x-5)^2$
D) $(2x-5)(2x+5)$

33. Which of the following is a factor of $x^2-1$ ?

A) $x-1$
B) $x+2$
C) $x-3$
D) $x+5$

34. Which topic is most closely connected with solving polynomial equations efficiently?

A) Bearings
B) Statistics
C) Factorization
D) Coordinate Geometry

“`html

35. The expression $9x^2-49$ can be factorized as:

A) $(3x-7)(3x+7)$
B) $(9x-7)(x+7)$
C) $(3x-7)^2$
D) $(9x+7)(x-7)$

36. Which expression is completely factorized?

A) $x^2-4$
B) $2x+6$
C) $x^2+5x+6$
D) $2(x-1)(x+3)$

37. The factorization of $x^2+x-6$ is:

A) $(x+2)(x+3)$
B) $(x+3)(x-2)$
C) $(x-3)(x-2)$
D) $(x+6)(x-1)$

38. When simplifying an algebraic fraction, common factors should be cancelled only after:

A) Adding the numerator and denominator
B) Squaring both expressions
C) Factorizing the numerator and denominator
D) Expanding all brackets

39. The HCF of $14a^2b$ and $21ab^3$ is:

A) $7ab$
B) $14ab$
C) $7a^2b^3$
D) $42ab^3$

40. Which identity is used to expand $(a-b)^2$ ?

A) $a^2-b^2$
B) $a^2+2ab+b^2$
C) $(a+b)(a-b)$
D) $a^2-2ab+b^2$

41. If $(x+4)$ is a factor of a polynomial, then substituting $x=-4$ gives:

A) 4
B) 0
C) -4
D) 1

42. The least common multiple is mainly used when:

A) Expanding identities
B) Finding square roots
C) Adding or subtracting algebraic fractions
D) Drawing graphs

43. Which expression has a common factor of $5x$ ?

A) $10x^2+15x$
B) $6x+9$
C) $8x^2+12$
D) $3x+7$

44. The factorization of $x^2-2x-15$ is:

A) $(x-5)(x-3)$
B) $(x+5)(x+3)$
C) $(x-5)(x+3)$
D) $(x+5)(x-3)$

45. Which statement about factorization is correct?

A) Every polynomial has only one factor.
B) Factorization expresses an expression as a product of simpler expressions.
C) Factorization always increases the degree of a polynomial.
D) Factorization is used only in geometry.

46. The expression $a^2+ab$ can be factorized as:

A) $a(a+b)$
B) $a(a-b)$
C) $(a+b)^2$
D) $ab(a+b)$

47. The LCM of $4x$ and $6x^2$ is:

A) $12x$
B) $24x$
C) $12x^2$
D) $24x^2$

48. Which of the following is a binomial?

A) $5x$
B) $x^2+2x+1$
C) $7$
D) $x+4$

49. Which identity helps in factorizing $a^2-2ab+b^2$ ?

A) $(a+b)^2$
B) $(a-b)^2$
C) $a^2-b^2$
D) $a(a+b)$

50. The primary purpose of algebraic manipulation is to:

A) Simplify expressions and make problems easier to solve
B) Increase the number of variables
C) Avoid using mathematical identities
D) Convert algebra into geometry

📚 Explore More Class 9 FBISE MCQs

Leave a Comment Cancel Reply