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

Q1: The common factor of x²y² and x³y³ is
(a) x²y²
(b) x³y³
(c) x²y³
(d) x³y2

View Answer

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

Q2: The common factor of x³y² and x⁴y is
(a) x⁴³y²
(b) x⁴y
(c) x³y²
(d) x³y

View Answer

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

Q3: The common factor of a²m⁴ and a⁴m² is
(a) a⁴m⁴
(b) a²m²
(c) a²m⁴
(d) a⁴m²

View Answer

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

Q4: The common factor of 2x, 3x³, 4 is
(a) 1
(b) 2
(c) 3
(d) 4

View Answer

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

Q5: The common factor of 10ab, 30bc, 50ca is
(a) 10
(b) 30
(c) 50
(d) abc

View Answer

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

Q6: The common factor of 14a²b and 35a⁴b² is
(a) a⁴b²
(b) 35a⁴b²
(c) 14a²b
(d) 7a²b

View Answer

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

Q7: The common factor of 72x³y⁴z⁴, 120z²d⁴x⁴ and 96y³z⁴d⁴ is
(a) 96z³
(b) 120z³
(c) 72z³
(d) 24z²

View Answer

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

Q8: The factorisation of 12a²b + 15ab² is
a) 3ab (4a + 5b)
(b) 3a²b (4a + 5b)
(c) 3ab² (4a + 5b)
(d) 3a²b² (4a + 5b)

View Answer

Ans: (a)
12a²b + 15ab² = 3ab(4a + 5b)

Q9: The factorisation of x²yz + xy²z + xyz² is
(a) xyz(x + y + z)
(b) x²yz(x + y + z)
(c) xy²z(x + y + z)
(d) xyz²(x + y + z)

View Answer

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

Q10: The factorisation of a (x + y + z) + b(x + y + z) + c(x + y + z) is
(a) (a + b + c)(x + y + z)
(b) (ab + bc + ca)(x + y + z)
(c) (xy + yz + zx)(a + b + c)
(d) none of these

View Answer

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

Q11: The factorisation of 6xy – 4y + 6 – 9x is
(a) (3x – 2)(2y – 3)
(b) (3x + 2)(2y – 3)
(c) (3x – 2)(2y + 3)
(d) (3x + 2)(2y + 3)

View Answer

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

Q12: The factorisation of x² + xy + 2x + 2y is
(a) (x + 2)(x + y)
(b) (x + 2)(x – y)
(c) (x – 2)(x + y)
(d) (x – 2)(x – y)

View Answer

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

Q13: The factorisation of ab – a – b + 1 is
(a) (a – 1)(b – 1)
(b) (a + 1)(b + 1)
(c) (a – 1)(b + 1)
(d) (a + 1)(b – 1)

View Answer

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

Q14: The factorisation of x² + x + xy + y + zx + z is
(a) (x + y + z)(x + 1)
(b) (x + y + z)(x + y)
(c) (x + y + z)(y + z)
(d) (x + y + z)(z + x)

View Answer

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

Q15: The factorisation of x² + 8x + 16 is
(a) (x + 2)²
(b) (x + 4)²
(c) (x – 2)²
(d) (x – 4)²

View Answer

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

Q16: The factorisation of 36x²y² – 1 is
(a) (6xy – 1)(6xy + 1)
(b) (6xy – 1)²
(c) (6xy + 1)²
(d) (6 + xy)²

View Answer

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

Q17: The value of (0.68)² – (0.32)² is
(a) -1
(b) 0
(c) 1
(d) 0.36

View Answer

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

Q18: The factorisation of 3x² + 10x + 8 is
(a) (3x + 4)(x + 2)
(b) (3x – 4)(x – 2)
(c) (3x + 4)(x – 2)
(d) (3x – 4)(x + 2)

View Answer

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

Q19: The factorisation of 6x² – 5x – 6 is
(a) (2x – 3)(3x + 2)
(b) (2x + 3)(3x + 2)
(c) (2x – 3)(3x – 2)
(d) (2x + 3)(3x – 2)

View Answer

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

Q20: The quotient of 28x² + 14x is
(a) 2
(b) 2x
(c) x
(d) x²

View Answer

Ans: (b)
MCQ (with Solutions): Factorisation | Mathematics (Maths) Class 8
= 2x

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FAQs on MCQ (with Solutions): Factorisation - Mathematics (Maths) Class 8

1. How can factorisation help in simplifying algebraic expressions?

Ans. Factorisation helps in simplifying algebraic expressions by breaking down the expression into its factors, making it easier to work with and solve. It also helps in finding common factors and simplifying complex expressions.

2. What are the different methods of factorisation in algebra?

Ans. Some common methods of factorisation in algebra include grouping, finding common factors, using the distributive property, and using special factorisation formulas such as the difference of squares or perfect square trinomials.

3. How can factorisation be used to solve algebraic equations?

Ans. Factorisation can be used to solve algebraic equations by factoring out common factors or applying factorisation methods to simplify the equation. This makes it easier to find the solutions or roots of the equation.

4. Can factorisation be used in real-life applications outside of algebra?

Ans. Yes, factorisation can be used in various real-life applications such as in economics, physics, engineering, and computer science. It helps in simplifying complex problems and finding optimal solutions.

5. What are the benefits of mastering factorisation in algebra?

Ans. Mastering factorisation in algebra can help improve problem-solving skills, enhance understanding of algebraic concepts, and make it easier to work with complex equations and expressions. It is a fundamental skill that is essential for further studies in mathematics.

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