AP 8th Class Maths Bits Chapter 12 Factorisation with Answers

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AP State Syllabus 8th Class Maths Bits 12th Lesson Factorisation with Answers

Choose the correct answer.

Question 1.
a² – 2ab + b² = ………………
A) (a – b)²
B) (a + b)²
C) a² – b²
D) (a + b) (a – b)
Answer:
A) (a – b)²

Question 2.
2 × 2 × 2 × 2 × 2 × 3 is a prime factorization of
A) 48
B) 72
C) 96
D) 84
Answer:
C) 96

Question 3.
Common factors of 6xy, 9y²
A) 3, y
B) 6, y²
C) 3, y²
D) 3, x, y
Answer:
A) 3, y

Question 4.
Factorise :15a³b – 35ab³
A) 5(a³b – 7ab³)
B) 5ab (3a² – 7b²)
C) 5a²b (3a² – 7b²)
D) 5ab (3a² – 7b)
Answer:
B) 5ab (3a² – 7b²)

Question 5.
Factorise : ax + ay + bx + by
A) (x + a) (y + b)
B) (x + y) (a + b)
C) (x + b) (y + a)
D) (xy + ab)
Answer:
B) (x + y) (a + b)

Question 6.
Factorisation of x² + 10x + 25
A) (x + 5) (x + 5)
B) (x + 2) (x + 5)
C) (x + 5) (x + 3)
D) (x + 4) (x + 5)
Answer:
A) (x + 5) (x + 5)

Question 7.
25p² – 49q² = ………………
A) (5p + 7q)²
B) (5p – 7q)²
C) (5p + 7q) (7q – 5p)
D) (5p + 7q) (5p – 7q)
Answer:
D) (5p + 7q) (5p – 7q)

Question 8.
(p + 4) (p – 4) (p² + 16) = …………….
A) p⁴ – 256
B) p² – 128
C) p² – 256
D) p⁸ – 256
Answer:
A) p⁴ – 256

Question 9.
x² + x (a + b) + ab = ……………….
A) (x + a) (x – b)
B) (x + a) (x + b)
C) (x – a) (x – b)
D) (x – 3) (x + b)
Answer:
B) (x + a) (x + b)

Question 10.
48a² – 243 b² = ………………
A) 3 (4a + 9b) (4a – 9b)
B) 3 (4a + 9b)
C) 3 (3a + 4b) (4a – 9b)
D) none
Answer:
A) 3 (4a + 9b) (4a – 9b)

Question 11.
Factors of m² – 4m – 21 ………………..
A) (m + 3)²
B) (m + 7) (m – 31)
C) (m – 7)²
D) (m – 7) (m + 3)
Answer:
D) (m – 7) (m + 3)

Question 12.
4x² + 20x – 96 = ……………….
A) (x + 8) (x – 3)
B) 4 (x + 8) (x – 3)
C) (x – 8) (x + 3)
D) (x – 3)²
Answer:
B) 4 (x + 8) (x – 3)

Question 13.
70 x⁴ ÷ 14 x² = ………………….
A) 5x
B) 5x^-3
C) \(\frac{\mathrm{x}^{2}}{2}\)
D) 5x²
Answer:
D) 5x²

Question 14.
(6a² + 30) ÷ (a +5) = ………
A) 6a
B) 3a
C) \(\frac{a}{3}\)
D) a
Answer:
A) 6a

Question 15.
(6x⁴ + 10x³ + 8x²) ÷ 2x² = …………….
A) 3x² – 5x + 1
B) 3x² + 5x + 4
C) x² – 5x + 11
D) x² + 5x + 1
Answer:
B) 3x² + 5x + 4

Question 16.
30 (a²bc + ab²c + abc²) ÷ 6abc = ………………
A) 5 (a + b + c)
B) 6 (a + b)
C) a + b + c
D) 3 (a – b)
Answer:
A) 5 (a + b + c)

Question 17.
x (3x² – 108) ÷ 3x (x – 6) = ……………..
A) x – 3
B) 6 + x
C) x + 6
D) 6 – x
Answer:
C) x + 6

Question 18.
(m² – 14 m – 32) ÷ (m + 2) = …………….
A) m – 3
B) m + 6
C) m – 6
D) m – 16
Answer:
D) m – 16

Question 19.
16 z² – 48 z + 36 = ……………….
A) 4 (2z – 3)²
B) (2z – 3)²
C) (4z – 3)²
D) None
Answer:
A) 4 (2z – 3)²

Question 20.
3x² + 6x²y + 9xy² = ………………
A) 3x (x – 2y)
B) 3 (2x + 3xy)
C) 3x (x + y)
D) 3x (x + 2xy + 3y²)
Answer:
D) 3x (x + 2xy + 3y²)

Question 21.
25a²b + 35ab² = ………………
A) 5ab (5a+ 7b)
B) 5ab (a – 2b)
C) 5ab (a – b)
D) 5a² b² (a – b)
Answer:
A) 5ab (5a+ 7b)

Question 22.
6ab + 12b = …………..
A) 6 (a + 2)
B) 6b (a + 2)
C) ab – 6
D) b (a – z)
Answer:
B) 6b (a + 2)

Question 23.
The prime factorization of 72 is ………………
A) 2³ × 3²
B) 3² × 2
C) 3 × 9²
D) 8 × 16²
Answer:
A) 2³ × 3²

Question 24.
0 ÷ 36 (x – 4) = ………………
A) 0
B) 6
C) 3
D) 10
Answer:
A) 0

Question 25.
(x + 3) (x + 6) = …………….
A) x² – 3x
B) x² + 9x + 18
C) x – 3x²
D) None
Answer:
B) x² + 9x + 18

Question 26.
11 xy² z³ ÷ 55 xyz = ……………..
A) \(\frac{x}{y^{2}}\)
B) \(\frac{5 z}{x}\)
C) \(\frac{y}{z}\)
D) \(\frac{\mathrm{yz}^{2}}{5}\)
Answer:
D) \(\frac{\mathrm{yz}^{2}}{5}\)

Question 27.
lx² + mx = ……………….
A) x² (m + x)
B) x (lx + m)
C) x + lm
D) l(x + m)
Answer:
B) x (lx + m)

Question 28.
(l – 8)² = …………
A) l² – 16l + 64
B) l – 8l +8
C) l – 16l² + 0
D) l² – 16
Answer:
A) l² – 16l + 64

Question 29.
81² – 3⁸ = ………….
A) 81
B) 16
C) 0
D) 19
Answer:
C) 0

Question 30.
x² – 2 + \(\frac{1}{x^{2}}\) = …………….
A) (x – \(\frac{1}{x}\))²
B) (\(\frac{1}{x}\) – 3)²
C) (3x – \(\frac{1}{x}\))²
D) None
Answer:
A) (x – \(\frac{1}{x}\))²

Question 31.
(a + b)³ – 3ab (a + b) = ……………..
A) a³ + b³
B) a³ -b³
C) a – b³
D) 3a-b
Answer:
A) a³ + b³

Question 32.
\(\frac{8.47 \times 8.47-1.53 \times 1.53}{6.94}\) = ……………
A) 16
B) 10
C) 30
D) 11
Answer:
B) 10

Question 33.
(3x – 2y)² – (3x -2y)² = …………
A) 2xy²
B) 7y²
C) 9x²
D) 0
Answer:
D) 0

Question 34.
4x + 1 is a factor of …………..
A) x² – 16
B) 16x – 3
C) 10x – 3
D) 16x² – 1
Answer:
D) 16x² – 1

Question 35.
(2a + 1) (\(\frac{1}{2 a-1}\) , –\(\frac{2}{4 a^{2}-1}\)) = ……………
A) -1
B) – 3
C) 1
D) 2
Answer:
C) 1

Question 36.
x² – 7 = …………….
A) (x + 7) (x – 7)
B)(x + √7)(x – √7)
C) (x – 3) (x + 4)
D) None
Answer:
B)(x + √7)(x – √7)

Question 37.
x + \(\frac{1}{x}\) = 6 then x² + \(\frac{1}{x^{2}}\) = ………………
A) 19
B) 16
C) 34
D) 10
Answer:
C) 34

Question 38.
In the above problem x⁴ + \(\frac{1}{x^{4}}\)= ……………..
A) 1154
B) 1145
C) 1123
D) 1192
Answer:
A) 1154

Question 39.
a⁴ – 81 = …………..
A) (a – 3) (a + 3) (a² + 9)
B) (a – 3)² (a² + 1)
C) (a – 3)⁴ (a + 1)
D) None
Answer:
A) (a – 3) (a + 3) (a² + 9)

Question 40.
7a (5x – 3y) + 5b (5x – 3y) = …………..
A) (5x – 3) (7a – 5)
B) (5x-3y) (7a + 5b)
C) (5x – 3) (4x – 1)
D) (5x – y) (7x – 3)
Answer:
B) (5x-3y)(7a + 5b)

Question 41.
ar + br + at + bt = …………..
A) (r + t) (b – a)
B) (r – t) (r + a)
C) (r + t) (a +b)
D) (r – t) (a – b)
Answer:
C) (r + t) (a +b)

Question 42.
(6 + p + q)(6 – p – q) = ………….
A) 36 – p² – q² – 2pq
B) 36 – 2p + q
C) 36 – 2p -2q
D) 36 – p² – q²
Answer:
A) 36 – p² – q² – 2pq

Question 43.
9x² – 256 = ……………..
A) (3x + 16)²
B) (3x + 16)(3x – 16)
C) (3x – 6)²
D) (x – 16)(3x – 1)
Answer:
B) (3x + 16)(3x – 16)

Question 44.
(3a – b)² – 9c² = ………….
A) (3a + b) (3c – b)
B) (3a – b + 3c) (3a – b – 3c)
C) (3a – b – c)²
D) (3a – b – 3c) (a – b)
Answer:
B) (3a – b + 3c) (3a – b – 3c)

Question 45.
(8 + x) (14 – x) = …………….
A) 121 – (x – 3)²
B) 12 – (x – 3)²
C) 12 – (x – 31)²
D) 11 – (x- 12)²
Answer:
A) 121 – (x – 3)²

Question 46.
x⁴ – y⁴ = …………….
A) (x – y)² – xy
B) (x + y) (x – y²)
C) (x² + y²) (x² – y²)
D) (x + y²) (x² + y)
Answer:
C) (x² + y²) (x² – y²)

Question 47.
(4x + 51y + 1) (4x + 51y – 1) …………….
A) (4x – 5y)²
B) (4x – 5)²
C) (3x – y)²
D) None
Answer:
D) None

Question 48.
\(\frac{\mathbf{x}-\mathbf{y}}{\sqrt{\mathbf{x}}-\sqrt{\mathbf{y}}}\) = ……………..
A) √x + √y
B) √x – y
C) x – √y
D) 1 – y
Answer:
A) √x + √y

Question 49.
(\(\frac{3001}{6}\))² – (\(\frac{\mathbf{2 9 9 9}}{6}\))² = ………………
A) 333\(\frac {1}{3}\)
B) 343\(\frac {1}{2}\)
C) 243\(\frac {1}{2}\)
D) 712 \(\frac {1}{2}\)
Answer:
A) 333\(\frac {1}{3}\)

Question 50.
2⁴ × 3 = …………..
A) 481
B) 48
C) 78
D) 92
Answer:
B) 48

Question 51.
3 + 2 (9) = …………
A) 11
B) 21
C) 16
D) 19
Answer:
B) 21

Question 52.
2⁵ × 3 = ……………
A) 90
B) 31
C) 96
C) 69
Answer:
C) 96

Question 53.
Identify true statement from following:
A) 3 (x – 1) = 7
B) 3 (x – 4) = 3x – 3
C) (x – 1)² = 9
D) x² – 3xy
Answer:
B) 3 (x – 4) = 3x – 3

Question 54.
(x + 8) ² = x² + □ + 64
A) 6x
B) 4x
C) 16x
D) \(\frac{x}{4}\)
Answer:
C) 16x

Question 55.
(b + 1) (3a + 2) = …………..
A) 3ab – 2b + 1
B) 3ab – 2
C) 3ab + 2
D) 3ab + 3a + 2b + 2
Answer:
D) 3ab + 3a + 2b + 2

Question 56.
(a² + 5) ÷ a² + 5 = ……………
A) 4
B) 5
C) 1
D) 2
Answer:
C) 1

Question 57.
Common factors of 8x, 24 are
A) 1, 2, x
B) 2, 4, x
C) 2, 4, 8
D) 8, 4, 3
Answer:
C) 2, 4, 8

Question 58.
(m – n) (m + 4) = ……………..
A) m² – n
B) m² – mn + 4m – 4n
C) m + n²
D) m² – 4mn + 1
Answer:
B) m² – mn + 4m – 4n

Question 59.
t (u + at) = …………..
A) ut + at²
B) t + at²
C) t – at²
D) ut – t²
Answer:
A) ut + at²

Question 60.
(49x – 63) ÷ 7 = …………….
A) 7x + 1
B) 7x – 9
C) x + 3
D) x – 79
Answer:
B) 7x – 9

Question 61.
x – y = ………….
A) x√y – 1
B) (√x – √y)(√x + √y)
C) (x – √y)(x – √y)
D) (√x – y)²
Answer:
B) (√x – √y)(√x + √y)

Question 62.
a² – b⁴ = …………..
A) (a – b) (a – b²)
B) (a + b) (a + 1)
C) (a – b) (a² – 1)
D) None
Answer:
D) None

Question 63.
(x + 2) (x² + 5) = ……………..
A) x³ + 2x² + 5x + 10
B) x³ – x² – 5x + 1
C) x³ – 7x² + 3
D) x³ – 3x + 7
Answer:
A) x³ + 2x² + 5x + 10

Question 64.
14x² ÷ 42x² = …………….
A) \(\frac{3}{x}\)
B) \(\frac{1}{x}\)
C) \(\frac{3}{x}\)
D) \(\frac{x}{3}\)
Answer:
D) \(\frac{x}{3}\)

Question 65.
If we divide x^2a – 1 by x^a – 1 we get ……………..
A) x – 1
B) x^a – 1
C) x + a
D) x^a + 1
Answer:
D) x^a + 1

Question 66.
If x² + \(\frac{1}{x^{2}}\) = 62 then x + \(\frac{1}{x}\) = ……….. (x + \(\frac{1}{x}\) > 0)
A) 3
B) 8
C) 4
D) 6
Answer:
B) 8

Question 67.
x⁴ – 1 ÷ x – 3 = ……………..
A) x³ – 1
B) x + 1
C) (x – 2)²
D) None
Answer:
D) None

Question 68.
18 a² b² c ÷ (- 6 abc) = …………….
A) – 3ab
B) \(\frac{-a b}{c}\)
C) abc²
D) ab
Answer:
A) – 3ab

Question 69.
The degree of a polynomial is 6 and the degree of other polynomial is 2 then the degree of the sum of the both polynomials is ……………….
A) 2
B) 4
C) 8
D) 6
Answer:
D) 6

Question 70.
(9x² – 12x – 12) ÷ (3x + 2) = ……………..
A) 3x + 1
B) 3x – 6
C) 6x – 1
D) 6x – 3
Answer:
B) 3x – 6