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16p³ -4p can be written as 4p (4p² – 1)

By using the formula a² – b² = (a+b) (a-b)

Now solving for the above equation

4p (4p² – 1) 

= 4p ((2p)² – (1)²)

= 4p (2p+1) (2p-1)

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Class 8 Maths MCQ Questions of Factorisation with answers are available online for students. The chapter-wise Multiple Choice Questions are provided at Sarthaks eConnect to make all students learn each concept and help them to score best marks in exams. Also, learn important MCQ Questions of Factorisation Class 8 with answers provided with detailed solutions.

Practice MCQ Question for Class 8 Maths chapter-wise

1. The common factor of x²y² and x³y³ is

(a) x²y²
(b) x³y³
(c) x²y³
(d) x³y²

2. The common factor of x³y² and x⁴y is

(a) x⁴³y²
(b) x⁴y
(c) x³y²
(d) x³y

3. The common factor of a²m⁴ and a⁴m² is

(a) a⁴m⁴
(b) a²m²
(c) a²m⁴
(d) a⁴m²

4. The common factor of 2x, 3x³, 4 is

(a) 1
(b) 2
(c) 3
(d) 4

5. The common factor of 10ab, 30bc, 50ca is

(a) 10
(b) 30
(c) 50
(d) abc

6. The common factor of 14a²b and 35a⁴b² is

(a) a⁴b²
(b) 35a⁴b²
(c) 14a²b
(d) 7a²b

7. The common factor of 72x³y⁴z⁴, 120z²d⁴x⁴ and 96y³z4d⁴ is

(a) 96z³
(b) 120z³
(c) 72z³
(d) 24z²

8. The factorisation of 12a²b + 15ab² is

(a) 3ab (4a + 5b)
(b) 3a²b (4a + 5b)
(c) 3ab² (4a + 5b)
(d) 3a²b² (4a + 5b)

9. 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)

10. 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

11. 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)

12. 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)

13. 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)

14. 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)

15. The factorisation of x² + 8x + 16 is

(a) (x + 2)²
(b) (x + 4)²
(c) (x – 2)²
(d) (x – 4)²

16. The factorisation of 36x²y² – 1 is

(a) (6xy – 1)(6xy + 1)
(b) (6xy – 1)²
(c) (6xy + 1)²
(d) (6 + xy)²

17. The value of (0.68)² – (0.32)² is

(a) -1
(b) 0
(c) 1
(d) 0.36

18. 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)

19. 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)

20. The quotient of 28x² + 14x is

(a) 2
(b) 2x
(c) x
(d) x²

21. On factorising 14pq + 35pqr, we get:

(a) pq(14 + 35r)
(b) p(14q + 35qr)
(c) q(14p + 35pr)
(d) 7pq(2 + 5r)

22. Divide as directed: 52pqr (p + q) (q + r) (r + p) ÷104pq (q + r) (r + p)

(a) r(p+q)
(b) 1/2 r(p+q)
(c) 1/2
(d) none of these

23. The factors of 3m2 + 9m + 6 are:

(a) (m + 1) (m + 2)
(b) 3(m + 1) (m + 2)
(c) 6(m + 1) (m + 2)
(d) 9(m + 1) (m + 2)

24. The factors of m² – 256 are:

(a) (m + 4)²
(b) (m – 4)²
(c) (m – 4) (m+4)
(d) None of the above

25. The factors of 49p² – 36 are:

(a) (7p + 6)²
(b) (7p – 6)²
(c) (7p – 6 ) ( 7p + 6)
(d) None of the above

Answer:

1. Answer: (a) x²y²

Explanation: x²y² = x × x × y × y

x³y³ = x × x × x × y × y × y

2. Answer: (d) x³y

Explanation: x³y² = x × x × x × y × y

x⁴y = x × x × x × x × y

3. Answer: (b) a²m²

Explanation: a²m⁴ = a × a × m × m × m × m

a⁴m² = a × a × a × a × m × m

4. Answer: (a) 1

Explanation: 2x = 2 × x

3x³ = 3 × x × x × x

4 = 2 × 2

Hence the common factor is 1

5. Answer: (a) 10

Explanation: 10ab = 2 × 5 × a × b

30bc = 2 × 3 × 5 × b × c

50ca = 2 × 5 × 5 × c × a

Hence common factor is 2 x 5 = 10

6. Answer: (d) 7a²b

Explanation: 14a²b = 2 × 7 × a × a × b

35a⁴b² = 5 × 7 × a × a × a × a × b × b

7. Answer: (d) 24z²

Explanation: 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

8. Answer: (a) 3ab (4a + 5b)

Explanation:  12a²b + 15ab² 

= 3ab(4a + 5b)

9. Answer: (a) xyz(x + y + z)

Explanation: x²yz + xy²z + xyz² 

= xyz (x + y + z)

10. Answer: (a) (a + b + c)(x + y + z)

Explanation: a(x + y + z) + b(x + y + z) + c(x + y + z)

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

11. Answer: (a) (a + b + c)(x + y + z)

Explanation:  6xy – 4y + 6 – 9x

= 2y(3x – 2) – 3(- 2 + 3x)

= (3x – 2)(2y – 3)

12. Answer: (a) (x + 2)(x + y)

Explanation:  x² + xy + 2x + 2y

= x(x + y) + 2(x + y)

= (x + 2) (x + y).

13. Answer: (a) (a - 1)(b -1)

Explanation: ab – a – b + 1

= a(b – 1) – 1(b – 1)

= (a – 1)(b – 1)

14. Answer: (a) (x + y + z)(x + 1)

Explanation:  x² + x + xy + y + zx + z

= x(x + 1) + y(x + 1) + z(x + 1)

= (x + 1)(x + y + z)

15. Answer: (b) (x + 4)²

Explanation: x² + 8x + 16

= (x)² + 2 (x)(4) + (4)² ((a + b)² = a² + 2ab + b²))

= (x + 4)².

16. Answer: (a) (6xy – 1)(6xy + 1)

Explanation:  36x²y² – 1

= (6xy)² – (1)² ((a² - b²) = (a+b)(a-b))

= (6xy – 1)(6xy + 1)

17. Answer: (d) 0.36

Explanation: (0.68 + 0.32) (0.68 – 0.32) 

= 0.36.

18. Answer: (a) (3x + 4)(x + 2)

Explanation: 3x² + 10x + 8 

= 3x² + 6x + 4x + 8

= 3x(x + 2) + 4(x + 2)

= (x + 2)(3x + 4)

19. Answer: (a) (2x – 3)(3x + 2)

Explanation:  6x² – 5x – 6

= 6x² – 9x + 4x – 6

= 3x(2x – 3) + 2(2x – 3)

= (2x – 3)(3x + 2)

20. Answer: (b) 2x

Explanation:  \(\frac{28x^21}{14x}\)

\(=\frac{2\times2\times7\times x\times x}{2\times7\times x}\)

= 2x

21. Answer: (d) 7pq(2 + 5r)

Explanation: 14pq + 35pqr

= 2.7.p.q + 5.7.p.q.r

= 7pq(2 + 5r)

22. Answer: (b) 1/2 r(p+q)

Explanation:  52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)

\(=\frac{52\times p\times q\times r\times (p+q)\times(q+r)\times(r+p)}{52\times2\times p\times q\times(q+r)\times(r+p)}\)

= \(\frac{1}{2}r(p+q)\)

23. Answer: (b) (b) 3[(m + 1) (m + 2)]

Explanation: 3m² + 9m + 6

= 3(m² + 3m + 2)

= 3 [m² + m + 2m + 2]

= 3 [m(m + 1)+ 2( m + 1)]

= 3 [(m + 1) (m + 2)]

24. Answer: (d) None of the above

Explanation: m⁴ = (m²)² and 256 = (16)²

m⁴ – 256 

= (m²)² – (16)² 

= (m² – 16) (m² + 16)

m² – 16 

= m² – 42 

= (m – 4) (m + 4)

m⁴  – 256 

= (m – 4) (m + 4) (m² + 16)

25. Answer: (d) None of the above

Explanation:  49p² – 36 

= (7p)² – ( 6 )² 

= (7p – 6 ) ( 7p + 6) ((a² - b²) = (a+b)(a-b))

Click here Practice MCQ Question for Factorisation Class 8

x² + 4x + 3 = x² + 3x + x + 3

= x(x+3) + 1(x + 3)

= (x+3) (x+1)

Correct option is   A) 333 \(\frac{1}{3}\)

Correct option is (A) \(333\frac13\)

\((\frac{3001}6)^2-(\frac{2999}6)^2\) \(=\frac{3001^2-2999^2}{6^2}\)

\(=\frac{(3001+2999)(3001-2999)}{36}\)

\(=\frac{6000\times2}{36}=\frac{1000}3\)

\(=\frac{333\times3+1}3\)

\(=333+\frac13\)

= \(333\frac13\)

D) 3ab + 3a + 2b + 2

Correct option is (D) 3ab + 3a + 2b + 2

(b + 1) (3a + 2) = 3ab + 3a + 2b + 2

Correct option is  C) 16x

Correct option is (C) 16x

\((x+8)^2=x^2+2\times x\times8+8^2\)

\(=x^2+16x+64\)

\(\therefore\Box=16x\)

First find the two numbers whose sum= 1 and product= -132

Clearly, the numbers are 12 and 11

∴ we get, x² + x – 132 

= x² + 12x – 11x – 132

= x(x+12) – 11(x+12)

= (x+12) (x-11)

ax-5b+ab-5x

ax+ab-5b-5x

a (x+b)-5 (b+x)

(x+b)(a-5)

First find the two numbers whose sum= 5 and product= -104

Clearly, the numbers are 13 and 8

∴ we get, x² + 5x – 104 

= x² + 13x – 8x – 104

= x(x+13) – 8(x+13)

= (x+13) (x-8)

First find the two numbers whose sum= -23 and product=42

Clearly, the numbers are 21 and 2

∴ we get, x² – 23x + 42 

= x² – 21x – 2x + 42

= x(x-21) – 2(x-21)

= (x-21) (x-2)

a² + 2ab + b² – c² = (a² + 2ab + b²)- c² 

= (a + b)² - (c)² 

= (a + b + c) ( a + b - c)

625 – x⁴ = (25)² - (x²)² 

= (25 + x²) (25 - x²)

= (25 + x²) [(5)² - (x)²]

= (25 + x²) (5 + x) (5 + x)

x² – y² – 2x + 2y = (x² – y²) - 2(x - y)

= (x + y) (x - y) - 2(x - y)

= (x - y) (x + y)- 2)

8x²y – 18y³ = 2y(4x² - 9y²)

= 2y[(2x² - (3y)²]

= 2y(2x + 3y) (2x - 3y)

We solve by using the formula (a+b) ² = a² + b² + 2ab We get, 

x² + (4)² + 2 (x) (4) = (x+4)²

Correct option is  A) 0

Correct option is (A) 0

0 \(\div\) 36 (x – 4) \(=\frac0{36(x-4)}\) = 0 

B) x² + 9x + 18 

Correct option is (B) x² + 9x + 18

(x + 3) (x + 6) \(=x^2+6x+3x+18\)

= \(x^2+9x+18\)

Correct option is   D) \(\frac{yz^2}{5}\)

Correct option is (D) \(\frac{yz^2}5\)

\(11\,xy^2z^3\div55\,xyz\) \(=\frac{11\,xy^2z^3}{55\,xyz}\)

= \(\frac{yz^2}5\)

a³b - a²b² - b³ = b(a³ - a²b - b²)

6x²y + 9xy² + 4y³ = y(6x² + 9xy + 4y²)

x² – 9x + 8x – 72 

x(x – 9) + 8(x – 9) 

(x – 9)(x + 8)

4x² + 4x + 1 

Identity a² +2ab + b² =(a + b)² 

= (2x)² + (2)(x)(1) +1² 

= (2x +1)²

x² + 14x + 49 

Identity a² + 2ab + b² = (a + b)² 

= x² + 2 × x × 7 + 7² 

= (x + 7)²

L.H.S. = 3x + 2x = 5x ≠ R.H.S

The correct statement is 3x + 2x = 5x

L.H.S. = (a + 4) (a + 2) = (a)² + (4 + 2) (a) + 4 × 2 = a² + 6a + 8 ≠ R.H.S

The correct statement is (a + 4) (a + 2) = a² + 6a + 8

(2a + 3b) ( a – b) = 2a² – 3b²

L.H.S. = (2a + 3b) (a − b) = 2a × a + 3b × a − 2a × b − 3b × b = 2a² + 3ab − 2ab − 3b² = 2a² + ab − 3b² ≠ R.H.S.

The correct statement is (2a + 3b) (a − b) = 2a² + ab − 3b²

5 + 7x - 6x² = 5 + 10x - 3x(1 + 2x)

= 5(1 + 2x) -3x(1 + 2x)

= (1 + 2x) (5 - 3x)

(a) For x = −3,

x² + 5x + 4 = (−3)² + 5 (−3) + 4 

= 9 − 15 + 4 = 13 − 15 = −2

(b) For x = −3,

x² − 5x + 4 = (−3)² − 5 (−3) + 4 

= 9 + 15 + 4 = 28

(c) For x = −3,

x² + 5x = (−3)² + 5(−3) 

= 9 − 15 = −6

2a² - 7b - 17ab + 26b² 

= 2a² - 13ab - 4ab + 26b² 

= a(2a - 13b) - 2b (2a - 13b)

Correct option is  A) ut + at²

Correct option is (A) ut + at²

t (u + at) = \(ut+at^2\)

Correct option is  B) 7x – 9

Correct option is (B) 7x – 9

(49x – 63) \(\div\) 7 \(=\frac{49x-63}7=\frac{7(7x-9)}7\)

= 7x – 9

L.H.S = (y − 3)² = (y)² − 2(y)(3) + (3)²  [(a − b)² = a² − 2ab + b²]  = y² − 6y + 9 ≠ R.H.S

The correct statement is (y − 3)² = y² − 6y + 9

6 + 7b - 3b² = 6 + 9b - 2b - 3b² 

= 3(2 + 3b) -b(2 + 3b)

= (2 + 3b) (3 - b)

Correct option is  B) 8

Correct option is (B) 8

\(x^2+\frac1{x^2}\) = 62

\(\Rightarrow\) \(x^2+\frac1{x^2}+2=62+2\)

\(\Rightarrow\) \((x+\frac1x)^2=64=8^2\)

\(\Rightarrow\) \(x+\frac1x\) = 8  \((\because\) \(x+\frac1x\) > 0)

B) (√x – √y)(√x + √y)

Correct option is (B) (√x – √y)(√x + √y)

x – y \(=(\sqrt x)^2-(\sqrt y)^2\)

= \((\sqrt x-\sqrt y)(\sqrt x+\sqrt y)\)

Correct option is  D) x^a + 1

Correct option is (D) x^a + 1

\(\frac{x^{2a}–1}{x^a–1}=\frac{(x^a)^2–1^2}{x^a–1}=\frac{(x^a-1)(x^a+1)}{x^a–1}\)

= \(x^a+1\)

Correct option is  D) None

Correct option is (D) None

\(a^2-b^4=a^2-(b^2)^2\)

\(=(a-b^2)(a+b ^2)\)

A) x³ + 2x² + 5x + 10 

Correct option is (A) x³ + 2x² + 5x + 10

\((x+2)(x^2+5)\)

= \(x^3+2x^2+5x+10\)

4 + y - 14y² = 4 + 8y - 7y - 14y² 

= 4(1 + 2y) - 7y(1 + 2y)

= (1 + 2y) (4 - 7y)

Correct option is  A) (a – b)²

Correct option is (A) (a – b)²

\(a^2–2ab+b^2\) \(=a^2–ab-ab+b^2\)

= a(a-b) - b(a-b)

= (a-b) (a-b)

= \((a-b)^2\)

x² – x – 42 = (x + k) (x + 6)

⇒ x² – 7x + 6x – 42 = (x + k) (x + 6)

⇒x (x – 7) + 6 (x – 7) = (x + k) (x + 6)

⇒ (x – 7) (x + 6) = (x + k) (x + 6)

On comparison

k = – 7

1. ⇔ (a)

2. ⇔ (d)

3. ⇔ (b)

4. ⇔ (c)

4x² – a²

= (2x)² – a²

= (2x + a) (2x – a)

(x + 2) (x + 3)

= x² + (2 + 3)x + 2 × 3

= x² + 5x + 6

True

If x = 2 and y = – 1 then value of x² + 4xy + 4y² is 0.