# 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

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

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

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

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

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

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

Question 8.
A quadratic polynomial in one vari¬able has………….terms.
A) 1
B) 2
C) 3
D) 4
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 + $$\frac{x}{2}+\frac{1}{x}$$
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
B) 1

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

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

Question 17.
The polynomial of degree ‘n’ has ………… zeroes.
A) 1
B) n + 1
C) n – 1
D) n
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
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
A) 10

Question 20.
The remainder when 2x3 + 3x2 +4x + 5 is divided by (x – 2)
A) 31
B) 29
C) 36
D) 41
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
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
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
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
C) (9x2 + 5) (9x2 – 5)

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

Question 26.
(P2 + 2) (p2 – 2) =
A) p2 + 4
B) p4 – 4
C) p2 – 4
D) p4 + 4
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
A) 4x2 + 9x2 + 16z2 + 12xy + 24yz + 16xz

Question 28.
1023 =
A) 10404
B) 1061208
C) 1061206
D) 1061202
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
C) (x + y) (x2 – xy + y2)

Question 30.
(- 12)3 + (8)3 + (4)3 =
A) 1152
B) 1296
C) 1084
D) 1082
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
A) $$\frac{1}{x+1}$$

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

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

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

Question 35.
The value of p(t) = 5t2 – 6t + 7 at t = – 1 is
A) – 18
B) 16
C) 18
D) – 16
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
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
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
B) 28

Question 39.
If p(x) = x2 + 5x + 4, then p(- 4) =
A) 0
B) – 32
C) 40
D) – 20
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
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
C) 3x

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

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

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

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

Question 51.
The zero of the polynomial ax + b is
A) $$\frac{-b}{a}$$
B) $$\frac{a}{b}$$
C) – a
D) – b
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
C) 6

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

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

Question 55.
1012 =
A) 12001
B) 10001
C) 10201
D) 100201
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
B) 10

Question 57.
(1 + x) (1 + x) =
A) 2 + 2x
B) 1 + x2
C) 1 + x2 + 2x
D) 1 + x + 2x2
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)
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
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
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
B) -7

Question 62.
The factor of a – b – a2 + b2 is
A) a – b
B) a2 + b2
C) 2ab
D) 4ab
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
C) 368

Question 64.
The degree of Polynomial 3x2y3 + 4xy3 + 7 is….
A) 3
B) 5
C) 4
D) 7
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) $$-\frac { q }{ p }$$
D) $$-\frac { q }{ p }$$

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

(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
D) I

Question 68.
103 x 97
A) II
B) III
C) IV
D) I
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
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
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)
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.
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
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
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
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
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
A) y = 8x

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

(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
D) 0

Question 80.
The remainder when x101 + 101 is divided by x + 1 is
A) 1
B) 100
C) 101
D) 0
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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($$-\frac{2}{3}$$)
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