Class 8 Maths – Factorisation MCQ

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Factorisation is an essential tool in algebra, allowing us to simplify expressions, solve equations, and better understand the structure of mathematical relationships. In essence, factorisation is the process of “breaking down” an algebraic expression into its most basic parts or “factors.” This simplification helps us manipulate and solve complex algebraic problems. To master this technique, one needs consistent practice and exposure to a variety of problems. Thus, let’s delve into a set of MCQs designed to test our understanding of factorisation!

1. What is the factorised form of x^2 – 9?

a) x^2 – 9
b) x^2 + 3x – 9
c) (x + 3)(x – 3)
d) (x + 9)(x – 9)

Answer:

c) (x + 3)(x – 3)

Explanation:

The expression is a difference of squares.

2. Which of the following expressions can be factorised as a(b + c)?

a) ab + bc
b) ab + ac
c) a + bc
d) ab + b + c

Answer:

b) ab + ac

Explanation:

Taking a common factor of 'a' we get a(b + c).

3. The common factor of 15x^2 and 45x is:

a) 15
b) 5x
c) 15x
d) x

Answer:

c) 15x

Explanation:

15x is the highest common factor.

4. What is the factorisation of 4x^2 + 8x?

a) 4x(x + 2)
b) 4x^2 + 8x
c) 2x(2x + 8)
d) x(4x + 8)

Answer:

a) 4x(x + 2)

Explanation:

Taking out the common factor of 4x.

5. Factorise: 9y^2 – 16

a) (3y – 4)(3y + 4)
b) 9y^2 – 16
c) (3y – 8)(3y + 8)
d) (9y + 16)(9y – 16)

Answer:

a) (3y – 4)(3y + 4)

Explanation:

This is a difference of squares.

6. Factorise: a^2 – b^2

a) (a – b)(a + b)
b) a^2 – b^2
c) (a + b)^2
d) (a – b)^2

Answer:

a) (a – b)(a + b)

Explanation:

This is a difference of squares.

7. Factorise: 5x + 15

a) 5(x + 3)
b) x(5 + 15)
c) 15(x + 5)
d) 5x + 15

Answer:

a) 5(x + 3)

Explanation:

Taking out the common factor of 5.

8. The common factor of 12x^3 and 16x^2 is:

a) 4x^2
b) 2x^2
c) 8x^2
d) 12x^2

Answer:

a) 4x^2

Explanation:

4x^2 is the highest common factor.

9. Which of the following is not factorisable?

a) x^2 + 6x + 9
b) x^2 – 1
c) 2x + 3
d) x^2 + x + 6

Answer:

d) x^2 + x + 6

Explanation:

The given expression doesn't have factors in the set of integers.

10. Factorise: x^2 + 10x + 25

a) (x + 5)(x + 5)
b) x^2 + 10x + 25
c) (x + 25)(x + 1)
d) (x + 10)(x + 2.5)

Answer:

a) (x + 5)(x + 5)

Explanation:

This is a perfect square trinomial.

11. What is the factorisation of 6x^2 + 15x?

a) x(6x + 15)
b) 6x^2 + 15x
c) 3x(2x + 5)
d) 15(x + 1)

Answer:

c) 3x(2x + 5)

Explanation:

Taking out the common factor of 3x.

12. Factorise: 7y^2 – 49

a) 7(y – 7)(y + 7)
b) 7y^2 – 49
c) (7y – 7)(7y + 7)
d) (7y – 49)(7y + 49)

Answer:

a) 7(y – 7)(y + 7)

Explanation:

This is a difference of squares after factoring out 7.

13. Which of the following is a common factor of 15x^3 and 5x^2?

a) 5x
b) x^2
c) 5x^2
d) 15x

Answer:

c) 5x^2

Explanation:

5x^2 is the highest common factor.

14. Factorise: 16x^4 – 81

a) (4x^2 – 9)(4x^2 + 9)
b) 16x^4 – 81
c) (8x^2 – 9)(8x^2 + 9)
d) (4x – 9)(4x + 9)

Answer:

a) (4x^2 – 9)(4x^2 + 9)

Explanation:

This is a difference of squares.

15. What is the factorised form of x^3 – 8?

a) (x – 2)(x^2 + 2x + 4)
b) x^3 – 8
c) (x – 2)(x^2 – 2x + 4)
d) (x + 2)(x^2 – 2x – 4)

Answer:

a) (x – 2)(x^2 + 2x + 4)

Explanation:

This is the difference of cubes.

16. Factorise: 4x^2 + 12x

a) 2x(2x + 6)
b) 4x(x + 3)
c) x(4x + 12)
d) 4x^2 + 12x

Answer:

b) 4x(x + 3)

Explanation:

Taking out the common factor of 4x.

17. Factorise: 25y^2 – 1

a) (5y + 1)(5y – 1)
b) 25y^2 – 1
c) (5y^2 + 1)(5y^2 – 1)
d) (25y + 1)(25y – 1)

Answer:

a) (5y + 1)(5y – 1)

Explanation:

This is a difference of squares.

18. Factorise: 3x^3 + 3x^2

a) 3x^2(x + 1)
b) x(3x^2 + 3)
c) 3x(x^2 + 1)
d) 3x^3 + 3x^2

Answer:

a) 3x^2(x + 1)

Explanation:

Taking out the common factor of 3x^2.

19. Which of the following is a factor of x^2 – 4x?

a) x + 4
b) x
c) x – 4
d) x^2

Answer:

b) x

Explanation:

'x' is a common factor.

20. What is the factorisation of x^2 – 6x + 9?

a) (x – 3)(x – 3)
b) (x – 6)(x + 1.5)
c) x^2 – 6x + 9
d) (x – 9)(x + 1)

Answer:

a) (x – 3)(x – 3)

Explanation:

This is a perfect square trinomial.

Related MCQ (Multiple Choice Questions) :

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