AP 9th Class Maths Bits Chapter 2 Polynomials and Factorisation with Answers

Practice the AP 9th Class Maths Bits with Answers Chapter 2 Polynomials and Factorisation on a regular basis so that you can attempt exams with utmost confidence.

AP State Syllabus 9th Class Maths Bits 2nd Lesson Polynomials and Factorisation with Answers

Choose the correct answer :

Question 1.
A polynomial with two terms is called
A) monomial
B) binomial
C) trinomial
D) multinomial
Answer:
B) binomial

Question 2.
For a polynomial p(x) if p(a) = 0 then a is called a…………….of the polynomial.
A) variable
B) zero
C) coefficient
D) term
Answer:
B) zero

Question 3.
The degree of the polynomial 7x²y⁴ + 3x²y² – 8
A) 4
B) 8
C) 6
D) 1
Answer:
C) 6

Question 4.
The degree of the polynomial (x² + 2x³) (x² – 5x²y² + y⁴) is
A) 3
B) 4
C) 2
D) 7
Answer:
D) 7

Question 5.
The coefficient of x² in (2x – 8) (7 – 3x) is
A) 2
B) 3
C) 6
D) – 6
Answer:
D) – 6

Question 6.
The zero of the polynomial 2x – 3 is
A) 3
B) \(\frac { 2 }{ 3 }\)
C) \(\frac { -3 }{ 2 }\)
D) \(\frac { 3 }{ 2 }\)
Answer:
D) \(\frac { 3 }{ 2 }\)

Question 7.
2x³ + 7x² – 8 is a
A) monomial
B) binomial
C) trinomial
D) zero
Answer:
C) trinomial

Question 8.
A quadratic polynomial in one vari¬able has………….terms.
A) 1
B) 2
C) 3
D) 4
Answer:
C) 3

Question 9.
Which of the following expressions is a polynomial ?
A) 3x^-2 + 7x + 1
B) 7x² + \(\frac{2}{\mathrm{x}}\) – 8
C) x² – x – 1
D) x² + \(\frac{x}{2}+\frac{1}{x}\)
Answer:
C) x² – x – 1

Question 10.
The value of p(x) = 7x² + 2x – 8 when x = 1
A) – 1
B) 1
C) 2
D) 17
Answer:
B) 1

Question 11.
The value of 5x² + 6x + 7 at x = -1
A) 18
B) – 6
C) 6
D) 0
Answer:
C) 6

Question 12.
Zeroes of the polynomial 9x² – 12x + 4 are
A) \(\frac{2}{3}, \frac{2}{3}\)
B) \(\frac{3}{2}, \frac{-3}{2}\)
C) \(\frac{-3}{2}, \frac{-3}{2}\)
D) (3,2)
Answer:
A) \(\frac{2}{3}, \frac{2}{3}\)

Question 13.
Zeros of the polynomial x² – 7x + 10 are
A) (2,-5)
B) (-2, 5)
C) (- 2,-5)
D) (2, 5)
Answer:
D) (2, 5)

Question 14.
The number of zeroes of the polynomial \(\frac{7 x}{3}=\) = -5
A) 1
B) 2
C) 3
D) many
Answer:
A) 1

Question 15.
The number of zeroes of a quadratic equation
A) 1
B) 2
C) 3
D) many
Answer:
B) 2

Question 16.
If 2 is a zero of the polynomial 2x² – 3x – a then a =
A) 2
B) – 2
C) – 3
D) 4
Answer:
A) 2

Question 17.
The polynomial of degree ‘n’ has ………… zeroes.
A) 1
B) n + 1
C) n – 1
D) n
Answer:
D) n

Question 18.
If (x – 2) is a factor of 2x³ + 3x² – 8x + k then the value of k is
A) 12
B) – 12
C) 24
D) 44
Answer:
B) – 12

Question 19.
The remainder when x³ + 2x² + 3x + 4 is divided by (x – 1) is
A) 10
B) 6
C) 4
D) 2
Answer:
A) 10

Question 20.
The remainder when 2x³ + 3x² +4x + 5 is divided by (x – 2)
A) 31
B) 29
C) 36
D) 41
Answer:
D) 41

Question 21.
The remainder when 3x²+ 2x – 6 is divided by (2x – 1)
A) \(\frac{-37}{8}\)
B) \(\frac{-43}{8}\)
C) \(\frac{59}{3}\)
D) None
Answer:
A) \(\frac{-37}{8}\)

Question 22.
The value of p if px⁴ + 7x² – 18 is divisible by (x – 3)
A) \(\frac{9}{5}\)
B) \(\frac{-5}{9}\)
C) \(\frac{5}{9}\)
D) 1
Answer:
B) \(\frac{-5}{9}\)

Question 23.
The expansion of (5x – 1)² is
A) 25x² – 5x + 1
B) 25x² – 10x – 1
C) 25x² – 10x +1
D) 25x² + 10x + 1
Answer:
C) 25x² – 10x +1

Question 24.
Factors of 81x⁴ – 25 are
A) (9x² + 5)²
B) (9x² – 5)²
C) (9x² + 5) (9x² – 5)
D) None
Answer:
C) (9x² + 5) (9x² – 5)

Question 25.
103 x 97 =
A) 9991
B) 9791
C) 10197
D) 9997
Answer:
A) 9991

Question 26.
(P² + 2) (p² – 2) =
A) p² + 4
B) p⁴ – 4
C) p² – 4
D) p⁴ + 4
Answer:
B) p⁴ – 4

Question 27.
(2x + 3y + 4z)² =
A) 4x² + 9x² + 16z² + 12xy + 24yz + 16xz
B) 2x² + 34y² + 4z² + 6xy + 12yz + 8xz
C) 4x² + 9y² + 16z²
D) 4x² + 9y² + 16z² + xy + yz + zx
Answer:
A) 4x² + 9x² + 16z² + 12xy + 24yz + 16xz

Question 28.
102³ =
A) 10404
B) 1061208
C) 1061206
D) 1061202
Answer:
B) 1061208

Question 29.
x³ – y³ =
A) (x – y) (x² – xy – y²)
B) (x – y) (x² + xy + y²)
C) (x + y) (x² – xy + y²)
D) None
Answer:
C) (x + y) (x² – xy + y²)

Question 30.
(- 12)³ + (8)³ + (4)³ =
A) 1152
B) 1296
C) 1084
D) 1082
Answer:
A) 1152

Question 31.
Which of the following expressions is not a polynomial ?
A) \(\frac{1}{x+1}\)
B) 7
C) x² – 3
D) x² – 4x + 5
Answer:
A) \(\frac{1}{x+1}\)

Question 32.
The degree of the polynomial
3x²y³ + 4xy + 7 is
A) 2
B) 3
C) 5
D) 1
Answer:
C) 5

Question 33.
The coefficient of \(\sqrt{2}\) x² in x² + 5 x – 1 is
A) 5
B) – 1
C) 0
D) 72
Answer:
C) 0

Question 34.
An example for constant polynomial is
A) 0
B) – 12
C) 3x – 4
D) x² + 2x – 1
Answer:
B) – 12

Question 35.
The value of p(t) = 5t² – 6t + 7 at t = – 1 is
A) – 18
B) 16
C) 18
D) – 16
Answer:
C) 18

Question 36.
The number of zeroes of a polynomial of degree ‘n’ will have
A) n – 1
B) n + 1
C) 0
D) n
Answer:
D) n

Question 37.
The identity used in simplifying 101 x 99 is
A) (a + b) (a – b) = a² – b²
B) (a – b)² = a² – 2ab + b²
C) (a + b)² = a² + 2ab + b²
D) (x + a) (x + b) = x² + (a + b)x + ab
Answer:
A) (a + b) (a – b) = a² – b²

Question 38.
If x = 2, then the value of (x + 5) (x + 2)
A) 40
B) 28
C) 20
D) x² + 7x + 10
Answer:
B) 28

Question 39.
If p(x) = x² + 5x + 4, then p(- 4) =
A) 0
B) – 32
C) 40
D) – 20
Answer:
A) 0

Question 40.
Zero of the polynomial p(x) = 3x + 1 is
A) \(\frac{1}{3}\)
B) – 2
C) \(\frac{-1}{3}\)
D) 3
Answer:
C) \(\frac{-1}{3}\)

Question 41.
The first term in quotient when you divide 3x² + x – 1 by x+1 is
A) 1
B) – 2
C) 3x
D) 3
Answer:
C) 3x

Question 42.
(x – 3) (x + 4) =
A) x² + x – 12
B) x² – x – 12
C) x² + 7x + 12
D) x² – 7x + 12
Answer:
A) x² + x – 12

Question 43.
If a + b + c = 0, then a³ + b³ + c³ =
A) O
B) 3abc
C) 3(a + b + c)
D) 3(a+b)(b+c)(c+a)
Answer:
B) 3abc

Question 44.
x³ – 8 =
A) (x – 2) (x – 2) ( x – 2)
B) (x – 2) (x² + 2x + 8)
C) (x – 2) (x² + 2x + 4)
D) (x – 2) (x² – 2x – 4)
Answer:
C) (x – 2) (x² + 2x + 4)

Question 45.
If f(x) is divided by (x – a), then the remainder is
A) f(-a)
B) f(l)
C) f(0)
D) f(a)
Answer:
D) f(a)

Question 46.
The factor of 3x² + x – 2 is
A) x – 1
B) 3x – 2
C) 3x + 2
D) 2x – 3
Answer:
B) 3x – 2

Question 47.
(x + y)² + (x – y)² =
A) 2(x² + y²)
B) 4xy
C) x² + y²
D) 2xy
Answer:
A) 2(x² + y²)

Question 48.
9x² – 25 =
A) (3x + 25) (3x – 1)
B) (9x – 1) (x + 25)
C) (3x + 5) (3x – 5)
D) (9x + 1) (x – 25)
Answer:
C) (3x + 5) (3x – 5)

Question 49.
One of the factors of 3x³ – 12x is
A) x – 1
B) 4x
C) x + 2
D) x + 1
Answer:
C) x + 2

Question 50.
The degree of the polynomial 7 – 2x³ + 7x²y + xy³ is
A) 4
B) 3
C) 2
D) 1
Answer:
A) 4

Question 51.
The zero of the polynomial ax + b is
A) \(\frac{-b}{a}\)
B) \(\frac{a}{b}\)
C) – a
D) – b
Answer:
A) \(\frac{-b}{a}\)

Question 52.
If 2 is a zero of the polynomial x² – kx + 8, then k =
A) 1
B) 4
C) 6
D) 3
Answer:
C) 6

Question 53.
The coefficient of x² in 7x³ – 2x² + 3x + 1 is
A) 7
B) – 2
C) 3
D) 1
Answer:
B) – 2

Question 54.
The coefficient of x³ in (2x – 3y) (4x² + 6xy + 9y²) is
A) 8
B) – 27
C) 12
D) 9
Answer:
A) 8

Question 55.
101² =
A) 12001
B) 10001
C) 10201
D) 100201
Answer:
C) 10201

Question 56.
The value of p(x) = 4x³ + 3x² + 2x + 1 at x = 1 is
A) 9
B) 10
C) 6
D) 7
Answer:
B) 10

Question 57.
(1 + x) (1 + x) =
A) 2 + 2x
B) 1 + x²
C) 1 + x² + 2x
D) 1 + x + 2x²
Answer:
C) 1 + x² + 2x

Question 58.
3y² + 2y – 5
A) (y – 1)(3y + 5)
B) (y + 1) (3y – 5)
C) (y – 1)(3y-5)
D) (y + 1) (3y + 5)
Answer:
A) (y – 1)(3y + 5)

Question 59.
(t-1)(t-1) =
A) t² + 1
B) t² – 2t + 1
C) t² + 2t + 1
D) t² – 1
Answer:
B) t² – 2t + 1

Question 60.
One of the factors of a³ – 3a²b + 3ab² – b³ is
A) – 3ab
B) 3ab
C) a + b
D) a – b
Answer:
D) a – b

Question 61.
If 2x³ – 2x² – 2x – 5 is divided by x + 1, then the remainder is
A) 0
B) -7
C) 6
D) -6
Answer:
B) -7

Question 62.
The factor of a – b – a² + b² is
A) a – b
B) a² + b²
C) 2ab
D) 4ab
Answer:
A) a – b

Question 63.
If a + b = 8, ab = 6 then the value of a³ + b³
A) 656
B) 576
C) 368
D) 638
Answer:
C) 368

Question 64.
The degree of Polynomial 3x²y³ + 4xy³ + 7 is….
A) 3
B) 5
C) 4
D) 7
Answer:
B) 5

Question 65.
The zero of the polynomial px + q is…
A) \(\frac { p }{ q }\)
B) \(\frac { q }{ p }\)
C) \(-\frac { p }{ q }\)
D) \(-\frac { q }{ p }\)
Answer:
D) \(-\frac { q }{ p }\)

Question 66.
Which of the following figure represent the algebrical identity (x – y)² = x² – 2xy + y² ?

Answer:
(B)

7-11 Questions:
I. (a + b)² = a² + 2ab + b²
ii. (a – b)² = a² – 2ab + b²
III. (a + b) (a – b) = a² – b²
V. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
VI. (a + b)³ = a³ + b³ + 3ab (a + b)
VII. (a – b)³ = a³ – b³ – 3ab (a – b)
Without actual multiplication which algebraic identity can be used to find the following:

Question 67.
99 x 99
A) II
B) III
C) I and II
D) I
Answer:
D) I

Question 68.
103 x 97
A) II
B) III
C) IV
D) I
Answer:
B) III

Question 69.
Expand (2a – 3b + 4c)²
A) 4a² – 9b² + 16c² – 12ab – 24bc + 16ac
B) 4a² + 9b² + 16c² – 12ab – 24bc + 16ca
C) 4a² – 9b² – 16c² – 12ab – 24bc + 16ca
D) 4a² + 9b² + 16c² – 12ab + 24bc + 16ac
Answer:
B) 4a² + 9b² + 16c² – 12ab – 24bc + 16ca

Question 70.
1 – 64a³ – 12a + 48a² is obtained by using which of the following identity:
A) IV
B) V
C) VII
D) III
Answer:
C) VII

Question 71.
x² – 5x + 6
A) (x – 3) (x – 2)
B) (x + 3) (x + 2)
C) (x – 3) (x + 2)
D) (x + 3) (x-2)
Answer:
A) (x – 3) (x – 2)

Question 72.
Assertion (A) : 6x⁵ + 5x⁴ + 3x² + \(\frac{4}{\mathrm{x}}\) + 5 is a polynomial of degree 5.
Reason (R) : Exponent of ‘x’ is negative integer, it is multinomial.
A) Both A and R are true but ‘R’ is not correct explanation of A.
B) A is correct, R is incorrect.
C) A is incorrect, R is correct.
D) Both A and R are true and ‘R’ is the correct explanation of A.
Answer:
B) A is correct, R is incorrect.

Question 73.
Match the following group A to B. Choose correct mapping of the following
Group – A — Group – B
i) (a + b)² – (a – b)² — A) 2(a² + b²)
ii) (a + b)² + (a – b)² — B) 2ab
iii) (a + b)² – (a² + b²) — C) 4ab
Choose the correct answer :
A) i – B, ii – C, iii – A
B) i – C, ii – A, iii – B
C) i – C, ii – B, iii – A
D) i – A, ii – B iii – C
Answer:
B) i – C, ii – A, iii – B

Question 74.
The degree of the polynomial (x³ + 7) (3 – x²) is
A) 3
B) 5
C) 6
D) 2
Answer:
B) 5

Question 75.
If length, breadth and height of the cuboid are (x – 1), (x – 10) and (x – 12) units, then volume of the cuboid in cubic units.

A) x³ + 23x² – 142x + 120
B) x³ – 23x² + 142x – 120
C) x³ – 23x² – 142x + 120
D) x³ + 23x² – 142x – 120
Answer:
B) x³ – 23x² + 142x – 120

Question 76.
The ratio of molecular weight of hy-drogen and oxygen in water is 1 : 8. (The relation between hydrogen and oxygen in linear equations in two vari-ables is). If the quantities of hydrogen and oxygen are ‘x’ and ‘y’
A) y = 8x
B) x + y = 8
C) xy = 8
D) x = 8y
Answer:
A) y = 8x

Question 77.
Which Geometrical figure related to Algebraic Identity
(x – y)² = x² + y² – 2xy ?

Answer:
(D)

Question 78.
If ‘2’ is the zero of the polynomial P(x) = 2x² – 3x + 7a, then the value of a is
A) \(\frac{-2}{7}\)
B) \(\frac{7}{2}\)
C) \(\frac{-7}{2}\)
D) \(\frac{2}{7}\)

Question 79.
If a + b + c’ = 6, then the value of (2 – a)³ + (2 – b)³ + (2 – c)³ – 3 (2 – a) (2 – b) (2 – c) is
A) -1
B) 1
C) 2
D) 0
Answer:
D) 0

Question 80.
The remainder when x¹⁰¹ + 101 is divided by x + 1 is
A) 1
B) 100
C) 101
D) 0
Answer:
A) 1

Question 81.
If p(x) = x + 3, then p(-x) + p(x) is equal to
A) 0
B) 3
C) 2x
D) 6
Answer:
A) 0

Question 82.
If 3 is zero of the polynomial x² + 2x – a, then “a” is
A) -3
B) -15
C) 15
D) 3
Answer:
C) 15

Question 83.
Statement A : Cubic polynomial has at most three zeroes.
Statement B : Degree of the zero poly-nomial is zero.
A) Both A and B are true
B) Both A and B are false
C) A is true and B is false
D) A is false and B is true
Answer:
A) Both A and B are true

Question 84.
The degree of the polynomial (y² + 7) (-y⁵ + 3) is
A) 5
B) 7
C) 10
D) -10
Answer:
B) 7

Question 85.
If the area of a square field is x² + y² + z² + 2xy – 2yz – 2zx sq. units, then its perimeter is
A) (x + y + z)²
B) 4 (x + y + z)
C) 4 (x + y – z)
D) (x + y – z)²
Answer:
C) 4 (x + y – z)

Question 86.
If x + 1 is a factor of polynomial 2x² + Kx then the value of K is
A) -4
B) -2
C) 2
D) +4
Answer:
C) 2

Question 87.
x + 1 is a factor of xⁿ + 1 only if
A) ‘n’ is an odd integer
B) ‘n’ is an even integer
C) ‘n’ is a negative integer
D) ‘n’ is a positive integer
Answer:
A) ‘n’ is an odd integer

Question 88.
If x² + 1 has no zeroes then ‘x’ is a
A) Real number
B) Natural number
C) Not Real
D) Integer
Answer:
C) Not Real

Question 89.
The volume of a cube is
x³ – 6x² + 12x – 8 then its edge in units
A) x – 4
B) x – 2
C) x + 2
D) x + 4
Answer:
B) x – 2

Question 90.
If x = 2 then the value of (x + 5) (x + 2) = ……………..
A) 28
B) 40
C) 20
D) x² + 7x + 10
Answer:
A) 28

Question 91.
The identity used in simplifying
103 x 97
A) (a + b)² = a² + 2ab + b²
B) (a – b)² = a² – 2ab + b²
C) (a – b) (a + b) = a² – b²
D) (x + a) (x + b) = x² + (a + b) x + ab
Answer:
C) (a – b) (a + b) = a² – b²

Question 92.
Which of the following is NOT a polynomial ?
A) 5
B) \(\sqrt{3}\)x² + 5y
C) \(\sqrt{x}\)
D) 3xyz
Answer:
C) \(\sqrt{x}\)

Question 93.
Which of the given polynomials has \(-\frac{2}{3}\) as its ‘zero’ ?
A) 2x + 3
B) 3x + 2
C) 2x – 3
D) 3x – 2
Answer:
B) 3x + 2

Question 94.
What is the value of ‘k’ if x – 3 is a factor of x³ – 2x² + k ?
A) 45
B) – 45
C) 9
D) – 9
Answer:
C) 9

Question 95.
The remainder when the polynomial f(x) in x is divided by 3x + 2 is ……………..
A) f(2)
B) f(-2)
C) f(\(\frac{2}{3}\))
D) f(\(-\frac{2}{3}\))
Answer:
D) f(\(-\frac{2}{3}\))

Question 96.
x² + y² + z² + 2xy – 2yz – 2zx =
A) (x + y + z)²
B) (x – y + z)²
C) (x + y – z)²
D) (x – y – z)²
Answer:
C) (x + y – z)²

Question 97.
Which of the given polynomials is of degree 3 ?
A) 3
B) 5xy
C) xyz
D) 3x² + 2x + 1
Answer:
C) xyz