Maths Quiz for Class 8 Factorisation

Maths Quiz for Class 8 Factorisation

In this post, we are providing 20 online maths quiz questions for class 8 factorisation. Online maths quiz will take around 20 minutes to complete it.

Question 1: Factorise 4x + 12y.

A) 4(3x + y)

B) 2(x + 3y)

C) 4(x + 3y)

D) (x + 3y)

Explanation: 4x + 12y = 4(x + 3y)

Question 2: Factorise 8xy + 6x²y².

A) 2xy(4 + 3xy)

B) 2xy(4 + xy)

C) 2xy(3 + 4xy)

D) xy(4 + 3xy)

Explanation: 8xy + 6x²y² = 2xy(4 + 3xy)

Question 3: Factorise a²bc + ab²c + abc².

A) abc(a + b + c)

B) ab(a + b + c)

C) ac(a + b + c)

D) bc(a + b + c)

Explanation: a²bc + ab²c + abc² = abc(a + b + c)

Question 4: Factorise 15x² + 20xy² + 10z².

A) 5(3x + 4y² + 2z²)

B) 5x(3x + 4y² + 2z²)

C) 5x(3x + 4y² + 2z)

D) 5x(3x + 4y + 2z²)

Explanation: 15x² + 20xy² + 10xz² = 5x(3x + 4y² + 2z²)

Question 5: Factorise 4ab + 6b + 6a + 9 by regrouping the terms.

A) (2a + 3) (2b + 2)

B) (2a + 3) (2b + 3)

C) (2a + 2) (2b + 3)

D) (2a + 3) (4b + 3)

Explanation: 4ab + 6b + 6a + 9 = (4ab + 6b) + (6a + 9) = 2b(2a + 3) + 3(2a + 3) = (2a + 3) (2b + 3)

Question 6: Factorise x² + x³ + x⁴ + x⁵ using regrouping.

A) (1 + x) (1 + x²)

B) x (1 + x) (1 + x²)

C) x² (1 + x) (1 + x²)

D) x² (1 + x) (1 + x³)

Explanation: x² + x³ + x⁴ + x⁵ = (x² + x³) + (x⁴ + x⁵) = x²(1 + x) + x⁴(1 + x) = (1 + x) (x² + x⁴) = (1 + x) x² (1 + x²) = x² (1 + x) (1 + x²)

Question 7: Factorise 12a²b + 16ab².

A) ab(3a + 4b)

B) 4ab(3a + 4b)

C) 4ab(4a + 4b)

D) 4ab(3a + 16b)

Explanation: 12a²b + 16ab² = 4ab(3a + 4b)

Question 8: Factorise 12xy + 8yz + 15px + 10zp using regrouping.

A) (3x + 4z) (4y + 5p)

B) (3x + 2z) (3y + 5p)

C) (3x + 2z) (4y + 3p)

D) (3x + 2z) (4y + 5p)

Explanation: 12xy + 8yz + 15px + 10zp = (12xy + 8yz) + (15px + 10zp) = 4y(3x + 2z) + 5p(3x + 2z) = (3x + 2z) (4y + 5p)

Question 9: Factorise 9x² + 24xy + 16y² using the identity (a + b)² = a² + 2ab + b².

A) (3x + 4y)2

B) (3x + y)2

C) (x + 4y)2

D) (3x + 4y + 6)2

Explanation: 9x² + 24xy + 16y² = (3x)² + 2 × 3x × 4y + (4y)² = (3x + 4y)²

Question 10: Factorise 25x² – 70xy + 49y² using the identity (a – b)² = a² – 2ab + b².

A) (x – 7y)2

B) (5x – y)2

C) (5x – 7y)2

D) (5x – 7y + 10)2

Explanation: 25x² – 70xy + 49y² = (5x)² – 2 × 5x × 7y + (7y)² = (5x – 7y)2

Question 11: Factorise 81p² – 256q² using a² – b² = (a + b) (a – b ).

A) (9p + 16q) (9p + 16q)

B) (9p + 16q) (9p – 16q)

C) (9p – 16q) (9p – 16q)

D) (9p + 16q) (p – q)

Explanation: 81p² – 256q² = (9p)² – (16q)² = (9p + 16q) (9p – 16q)

Question 12: Factorise 32p⁴ – 50q⁴.

A) 2(4p² + 5q²) (4p² + 5q²)

B) 2(4p² + 5q²) (4p² – 5q²)

C) (4p² + 5q²) (4p² – 5q²)

D) 2(4p² – 5q²) (4p² – 5q²)

Explanation: 32p⁴ – 50q⁴ = 2(16p⁴ – 25q⁴) = 2[(4p²)² – (5q²)²] = 2(4p² + 5q²) (4p² – 5q²)

Question 13: Factorise 16x⁴ – 81y⁴.

A) (4x² + 9y²) (2x + 3y) (2x – 3y)

B) (4x² + 9y²) (2x + 3y) (2x + 3y)

C) (4x² + 9y²) (2x – 3y) (2x – 3y)

D) (4x² + 9y²) (4x + 9y) (4x – 9y)

Explanation: 16x⁴ – 81y⁴ = (4x²)² – (9y²)² = (4x² + 9y²) (4x² – 9y²) = (4x² + 9y²) [(2x)² – (3y)²] = (4x² + 9y²) (2x + 3y) (2x – 3y)

Question 14: Factorise x² + 7x + 12 by splitting the middle term.

A) (x + 4) (x – 3)

B) (x + 3) (x + 3)

C) (x + 4) (x + 4)

D) (x + 4) (x + 3)

Explanation: x² + 7x + 12 = x² + (4 + 3)x + 12 = x² + 4x + 3x + 12 = x(x + 4) + 3(x + 4) = (x + 4) (x + 3)

Question 15: Factorise x² + 4x – 60 by splitting the middle term.

A) (x – 10) (x + 6)

B) (x – 10) (x – 6)

C) (x + 10) (x – 6)

D) (x + 10) (x + 6)

Explanation: x² + 4x – 60 = x² + (10 – 6)x – 60 = x² + 10x – 6x – 60 = x(x + 10) – 6(x + 10) = (x + 10) (x – 6)

Question 16: Factorise 7x² – 5x – 12 by splitting the middle term.

A) (x + 1) (7x + 12)

B) (x + 1) (7x – 12)

C) (x – 1) (7x – 12)

D) (x – 1) (7x + 12)

Explanation: Here, –12 × 7 = –84 and –12 + 7 = –5. Therefore, 7x² – 5x – 12 = 7x² + (7 – 12)x – 12 = 7x² + 7x – 12x – 12 = 7x(x + 1) – 12(x + 1) = (x + 1) (7x – 12)

Question 17: 42x²y²z² ÷ 6xyz = __________

A) 7xyz

B) 7x²yz

C) 7xy²z

D) 7xyz2

Explanation: 42x²y²z² ÷ 6xyz = 7x^2-1y^2-1z^2-1 = 7xyz

Question 18: (8x³ + 6x² + 2x) ÷ 2x = ____________

A) 4x² + 3x + 2

B) 4x² + 6x + 1

C) 4x² + 3x + 1

D) 4x² + 3x² + 1

Explanation: (8x³ + 6x² + 2x) ÷ 2x = 2x(4x² + 3x + 1) ÷ 2x = 4x² + 3x + 1

Question 19: Divide (x² + 9x + 20) by (x + 4).

A) x + 4

B) x + 5

C) x + 3

D) x + 2

Explanation: Let us factorise x² + 9x + 20 first. x² + 9x + 20 = x² + 5x + 4x + 20 = x(x + 5) + 4(x + 5) = (x + 4) (x + 5). Now, (x² + 9x + 20) ÷ (x + 4) = (x + 4) (x + 5) ÷ (x + 4) = x + 5

Question 20: Divide (3x² – 13x + 12) by (x – 3).

A) x – 4

B) 3x + 4

C) 3x – 4

D) x + 4

Explanation: Let us factorise 3x² – 13x + 12 first. 3x² – 13x + 12 = 3x² – 9x – 4x + 12 = 3x(x – 3) – 4(x – 3) = (x – 3) (3x – 4). Now, (3x² – 13x + 12) ÷ (x – 3) = (x – 3) (3x – 4) ÷ (x – 3) = 3x – 4

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