MCQ (with Solutions): Factorisation | Mathematics (Maths) Class 8 PDF Download

Ans: (a)
x²y² = x × x × y × y
x³y³ = x × x × x × y × y × y 

Hence, Common Factor of x²y² and x³y³ is x²y² 

Ans: (d)
x³y² = x × x × x × y × y
x⁴y = x × x × x × x × y

Hence, Common Factor of x³y² and x⁴y is x³y . 

Ans: (b)
a²m⁴ = a × a × m × m × m × m
a⁴m² = a × a × a × a × m × m

Hence, Common Factor of a²m⁴ and a⁴m² is  a²m² . 

Ans: (a)
2x = 2 × x
3x³ = 3 × x × x × x
4 = 2 × 2
Hence the common factor is 1 

Ans: (a)
10ab = 2 × 5 × a × b
30bc = 2 × 3 × 5 × b × c
50ca = 2 × 5 × 5 × c × a 

Hence the common factor is  10.

Ans: (d)
14a²b = 2 × 7 × a × a × b
35a⁴b² = 5 × 7 × a × a × a × a × b × b 

Hence the common factor of 14a²b and 35a⁴b² is 7a²b. 

Ans: (d)
72x³y⁴z⁴ = 2 × 2 × 2 × 3 × 3 × x × x × x × y × y × y × y × z × z × z × z.
120z²d⁴x⁴ = 2 × 2 × 2 × 3 × 5 × z × z × d × d × d × d × x × x × x × x
96y³z⁴d⁴ = 2 × 2 × 2 × 2 × 2 × 3 × y × y × z × z × z × z × d × d × d × d
Hence common factor is 2 x 2 x 2 x 3 = 24z² 

Ans: (a)
12a²b + 15ab²  = 3ab(4a + 5b) 

12a²b=2×2×3×a×a×b
15ab²=3×5×a×b×b

Common factors: 3×a×b 

Hence  factorisation of 12a²b + 15ab² is  3ab(4a+5b)

Ans: (a)
x²yz + xy²z + xyz² 
= xyz (x + y + z) 

Hence  factorisation of x²yz + xy²z + xyz² is  xyz(x + y + z). 

Ans: (a)
a(x + y + z) + b(x + y + z) + c(x + y + z)
= (x + y + z) (a + b + c). 

Hence  factorisation of a (x + y + z) + b(x + y + z) + c(x + y + z) is  (a + b + c)(x + y + z). 

Ans: (a)
6xy – 4y + 6 – 9x
= 2y(3x – 2) – 3(- 2 + 3x)
= (3x – 2)(2y – 3) 

Hence  factorisation of a (x + y + z) + b(x + y + z) + c(x + y + z) is  (a + b + c)(x + y + z). 

Ans: (a)
x² + xy + 2x + 2y
= x(x + y) + 2(x + y) = (x + 2) (x + y).

 Hence  factorisation of x² + xy + 2x + 2y is (x + 2)(x + y). 

Ans: (a)
ab – a – b + 1
= a(b – 1) – 1(b – 1)
= (a – 1)(b – 1) 

Hence  factorisation of  ab – a – b + 1 is (a – 1)(b – 1).

Ans: (a)
x² + x + xy + y + zx + z
= x(x + 1) + y(x + 1) + z(x + 1)
= (x + 1)(x + y + z) 

Hence  factorisation of  x² + x + xy + y + zx + z is (x + y + z)(x + 1).

Ans: (b)
x² + 8x + 16
= (x)² + 2 (x)(4) + (4)² ((a + b)² 
= a² + 2ab + b²))
= (x + 4)².

Hence  factorisation of  x² + 8x + 16 is (x + 4)².

Ans: (a)
36x²y² – 1
= (6xy)² – (1)² ((a² - b²)
= (a+b)(a-b))
= (6xy – 1)(6xy + 1)

 Hence  factorisation of 36x²y² – 1 is (6xy – 1)(6xy + 1)

Ans:  (d)
(0.68 + 0.32) (0.68 – 0.32)  
= 0.36.  

Hence  factorisation of (0.68)² – (0.32)² is 0.36.

Ans: (a)
3x2 + 10x + 8  
= 3x2 + 6x + 4x + 8
= 3x(x + 2) + 4(x + 2)
= (x + 2)(3x + 4)

 Hence  factorisation of 3x² + 10x + 8 is  (3x + 4)(x + 2)

Ans: (a)
6x² – 5x – 6
= 6x² – 9x + 4x – 6
= 3x(2x – 3) + 2(2x – 3)
= (2x – 3)(3x + 2) 

Hence  factorisation of  6x² – 5x – 6 is (2x – 3)(3x + 2)

Ans: (b)
=  2 × 2 × 7 × x × x2 × 7 × x 
= 2x