SMART EDUCATIONS
1 SMART EDUCATIONS ( www.smarteducations.org )
POLYNOMIALS
1.
๐ผ๐ ๐ฅ
51
+ 51 ๐๐ ๐๐๐ฃ๐๐๐๐ ๐๐ฆ ( ๐ฅ + 1 ) ๐กโ๐๐ ๐๐ก๐ ๐๐๐๐๐๐๐๐๐ ๐๐
a. 0 b. 1 c. 49 50. 50
2.
๐โ๐ ๐๐๐๐ก๐๐๐ ๐๐ ( 1 โ ๐ฅ
3
) ๐๐๐
a. b. c.
( 1 + ๐ฅ )( 1 โ ๐ฅ + ๐ฅ
2
) ( 1 โ ๐ฅ )( 1 + ๐ฅ + ๐ฅ
2
) ( 1 + ๐ฅ )( 1 โ ๐ฅ
2
)
d.
( 1 + ๐ฅ )( 1 + ๐ฅ
2
)
3.
๐โ๐ ๐ฃ๐๐๐ข๐ ๐๐ 249
2
โ 248
2
๐๐
a. b. 477 c. 487 d. 497
1
2
4. Abscissa of all the points on the y-axis is
a. 1 b. Any number c. 0 d. 2
5. Which of the following is a linear equation:
a.
๐ฅ
2
+ 2 ๐ฅ = 2 ๐ฅ
2
โ 3 ๐ฅ + 7
b.
( ๐ฅ + 2 )( ๐ฅ + 3 )= ๐ฅ
2
+ 6 ๐ฅ โ 8
c.
7 ๐ฅ + 3 = 7 ๐ฅ โ 7
d. None of these
6.
๐ฅ โ ๐ฅ
3
๐๐ ๐ ............................... ๐๐๐๐ฆ๐๐๐๐๐๐ .
a. Linear b. Quadratic c. Cubic d. None of the above
7. The coefficient of x in the expansion (x+3)
3
a. 1 b. 9 c. 18 d. 27
8.
๐ผ๐ 3 ๐ฅ +
1
2
( )
3 ๐ฅ โ
1
2
( )
= 9 ๐ฅ
2
โ ๐ ๐กโ๐๐ ๐กโ๐ ๐ฃ๐๐๐ข๐ ๐๐ ๐ ๐๐ :
a. 0 b. c. d.
โ
1
4
1
4
1
2
9.
๐ผ๐
๐
๐
+
๐
๐
=โ 1 ๐กโ๐๐ ๐
3
โ ๐
3
๐๐
a. -3 b. -2 c. 1 d. 0
10. Zero of the polynomial p(x) = 2x+5 is
a. b. c. d.
โ
5
3
โ
5
2
5
6
1
2
11. then the value of k is
๐ผ๐ ( ๐ฅ โ 2 ) ๐๐ ๐ ๐๐๐๐ก๐๐ ๐๐ ๐ ( ๐ฅ ) = ๐ฅ
3
โ 6 ๐ฅ + 2 ๐ ,
a. -2 b. 2 c. -6 d. -3
12.
๐ผ๐ ๐ ( ๐ฅ ) = 3 ๐ฅ โ 4 ๐ฅ
2
+ 6 , ๐กโ๐๐ ๐กโ๐ ๐ฃ๐๐๐ข๐ ๐๐ ๐ (โ 1 ) ๐๐
a. 2 b. 0 c. -1 d. 1
13. is a polynomial of degree
2
a. a. 2 b) 0 c) 1 d)
1
2
14. If p (x) = x+3 , then p (x) + p (-x) is equal to
a. 3 b. 0 c. 2x d. 6
15. The coefficient of x in the expansion of (x+3)
3
is
a. 1 b. 9 c. 18 d. 27
16. Degree of the polynomial 4x
4
+ 0x
3
+ 0x
5
+ 5x + 7 is
SMART EDUCATIONS
2 SMART EDUCATIONS ( www.smarteducations.org )
a. 4 b. 5 c. 3 d. 7
17. The remainder when x
4
+8x+5 is divided by x+4 is
a. 229 b. 134 c. -229 d. -234
18. The zero of the polynomial f(x) = 2x+7 is?
a. b. c. d.
7
2
โ 7
2
2
7
โ 2
7
19. The value of k, if (x-1) is a factor of 4x
3
+3x
2
-4x +k, is
a. 1 b. 2 c. -3 d. 3
20. is a polynomial of degree.
3
a. b. 0 c. 2 d. 1
1
2
21. Degree of zero polynomial is
a. 0 b. 1 c. any real number d. Not defined
22. The zeroes of the polynomial p(x) = x
2
-3x are
a. 0,0 b. 0,3 c. 0,-3 d. 3,-3
23. The polynomial of the type ax
2
+bx+c, a=0 is called
a. Linear polynomial b. Quadratic polynomial c. Cubic polynomial
d. Biquadratic polynomial
24. If x
2
+kx+6 =(x+2)(x+3) for all x, then the value of k is :
a. 1 b. -1 c. 5 d. 3
25.
๐๐๐๐ข๐ ๐๐ ( 256 )
0 . 16
ร( 256 )
0 . 09
=
a. 4 b. 16 c. 64 d. 256.25
26. The value of 249
2
- 248
2
is
a. 1 b. 487 c. 477 d. 497
27.
2 ๐๐ ๐ ๐๐๐๐ฆ๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐
a. 2 b. 0 c. 1 d. 3
28. One of the linear factors of is
3 ๐ฅ
2
+ 8 ๐ฅ + 5
a. x+1 b. x-2 c. x+2 d. x-4
29. For what value of k, (x+1) is a factor of
๐ ( ๐ฅ )= ๐ ๐ฅ
2
โ ๐ฅ + 4 ?
30.
๐น๐๐๐ก๐๐๐๐ ๐ : 2 ๐ฅ
5
+ 432 ๐ฅ
2
๐ฆ
3
.
31.
๐น๐๐๐ก๐๐๐๐ ๐ : 125 ๐ฅ
3
โ 343 ๐ฆ
3
.
32.
๐ผ๐ ๐ฅ
3
+ ๐ ๐ฅ
2
+ ๐๐ฅ + 6
( )
โ๐๐ ( ๐ฅ โ 2 ) ๐๐ ๐ ๐๐๐๐ก๐๐ ๐๐๐ ๐๐๐๐ฃ๐๐ ๐๐๐๐๐๐๐๐๐ 3 ๐คโ๐๐ ๐๐๐ฃ๐๐๐๐
by (x-3), find the values of a and b.
33. Find the value of the polynomial .
๐ ( ๐ฅ )= ๐ฅ
3
โ 3 ๐ฅ
2
โ 2 ๐ฅ + 6 ๐๐ก ๐ฅ = 2
34.
๐ผ๐ ( 3 ๐ฅ โ 15 )
0
๐๐๐ ๐ฅ + 5 ( )
0
๐๐๐ ๐๐๐๐๐๐๐๐๐๐ก๐๐๐ฆ ๐๐๐๐๐๐ , ๐๐๐๐ ๐กโ๐ ๐๐๐๐๐๐
35.
๐ธ๐ฃ๐๐๐ข๐๐ก๐ 99 ร 101 ๐ข๐ ๐๐๐ ๐ ๐ข๐๐ก๐๐๐๐ ๐๐๐๐๐ก๐๐ก๐ฆ .
36.
๐น๐๐๐ ' ๐ฅ ' , ๐๐ 2
๐ฅ โ 7
ร 5
๐ฅ โ 4
= 1250 .
37. Find the perimeter of the rectangle whose area is .
๐ฅ
2
โ 5 ๐ฅ + 6
38.
๐ผ๐ ๐ฅ
๐
= ๐ฆ , ๐ฆ
๐
= ๐ง ๐๐๐ ๐ง
๐
= ๐ฅ , ๐กโ๐๐ ๐๐๐๐ฃ๐ ๐กโ๐๐ก ๐๐๐ = 1
39.
๐น๐๐๐ก๐๐๐๐ ๐ : 4 ๐ฅ
2
+ 9 ๐ฆ
2
+ 16 ๐ง
2
+ 12 ๐ฅ๐ฆ โ 24 ๐ฆ๐ง โ 16 ๐ฅ๐ง .
SMART EDUCATIONS
3 SMART EDUCATIONS ( www.smarteducations.org )
40.
๐น๐๐๐ก๐๐๐๐ ๐ : ๐ฅ
4
+
1
๐ฅ
4
+ 1
41.
๐๐๐๐ฃ๐ ๐กโ๐๐ก ๐ฅ
3
+ ๐ฆ
3
+ ๐ง
3
โ 3 ๐ฅ๐ฆ๐ง = ๐ฅ + ๐ฆ + ๐ง ( ) ๐ฅ
2
+ ๐ฆ
2
+ ๐ง
2
โ ๐ฅ๐ฆ โ ๐ฆ๐ง โ ๐ฅ๐ง
( )
42. ๐น๐๐๐ก๐๐๐๐ ๐ : ๐ฅ
3
โ 3 ๐ฅ
2
โ 9 ๐ฅ โ 5
43. Find the value of a for which (x-a) is a factor of
๐ฅ
3
โ ๐ ๐ฅ
2
+ 2 ๐ฅ + ๐ โ 1
44. Evaluate
97 ร 102 ๐ข๐ ๐๐๐ ๐ ๐ข๐๐ก๐๐๐๐ ๐๐๐๐๐ก๐๐ก๐ฆ .
45. Find the area of the triangle, two sides of which are 8cm and 11cm and the perimeter is
32 cm.
46. ๐๐๐๐๐๐ฆ ๐ฅ
3
+ ๐ฆ
3
=( ๐ฅ + ๐ฆ )( ๐ฅ
2
+ ๐ฆ
2
โ ๐ฅ๐ฆ )
47.
๐ผ๐ ๐ + ๐ + ๐ = 0 , ๐ โ๐๐ค ๐กโ๐๐ก ๐
3
+ ๐
3
+ ๐
3
= 3 ๐๐๐
48.
๐น๐๐๐ก๐๐๐๐ ๐ : โ ( ๐ ) 3 ๐ฅ
2
โ ๐ฅ โ 4 ( ๐๐ ) 2 ๐ฅ
2
+ 7 ๐ฅ + 3
49. Factorise using appropriate identity:
๐ฆ
2
โ
๐ฆ
2
100
50. Without calculating the cubs, find the value of: (28)
3
+ (-15)
3
+ (-13)
3
.
51. Find the remainder if x
15
+ 51 is divided by X+1.
52. If p(x) =x- 4x + 3, then evaluate p (2) โ p (-1) + p (ยฝ).
53. Factorise: x
3
-3x
3
-9x โ 5.
54. If p
2
+ 4q
2
+ 9r
2
= 2pq+6qr+3pr, then prove that p
3
+8q
3
+27r
3
=18pqr.
55. Find the product with the suitable identity:-
๐ฅ +
1
๐ฅ
( )
๐ฅ โ
1
๐ฅ
( )
๐ฅ
2
+
1
๐ฅ
2
( )
๐ฅ
4
+
1
๐ฅ
4
( )
56. Compute the value of 9x
2
+4y
2
if xy = 6 and 3x+2y=12.
57. Factorise:-
a. x
2
-1-2a-a
2
b. .
๐ฅ
2
+
1
๐ฅ
2
+ 2 โ 2 ๐ฅ โ
2
๐ฅ
c. Check whether (7+3x) is a factor of (3x
3
+7x).
d. , then evaluate
๐ฅ โ
1
๐ฅ
( )
= 4
i.
๐ฅ
2
+
1
๐ฅ
2
( )
ii.
๐ฅ
4
+
1
๐ฅ
4
( )
58. 2x
3
+4x
2
-7ax-5 and 2x
3
+ax
2
-6x+3 are polynomials which on dividing by (x+1) and (x-1)
leaves remainders y and z respectively, if y-3z=16, then find a.
59. Give the geometric representations of 2x+9=0 as an equation
a. In one variable
b. In two variables
60. Find the remainder when x
4
+x
3
-2x
2
+x+1 is divided by x-1.
61. Find the value of k, if x-1 is a factor of 4x
3
+3x
2
-4x+k.
62. Factorise:- 6x
2
+17x+5
63. If x+y+z=0, show that x
3
+y
3
+z
3
=3xyz.
64. Factorise : 2y
3
+y
2
-2y -1
65. Find the value of the polynomial 5x-4x
2
+3 at x=2.
SMART EDUCATIONS
4 SMART EDUCATIONS ( www.smarteducations.org )
66. GIve possible expression for the length and breadth of the following rectangle if its area
is 35y
2
+13y-12.
67. Factorise: 8x
3
+27y
3
+36x
2
y+54xy
2
68. If a
2
+ b
2
and c
2
= 40 and ab+bc+ac=12, find the value of a
3
+b
3
+c
3
-3abc.
69. If
๐ฅ
2
+
1
๐ฅ
2
= 11 , ๐๐๐๐ ๐กโ๐ ๐ฃ๐๐๐ข๐ ๐๐ ๐ฅ
3
โ
1
๐ฅ
3
70. When the polynomial 4x
3
+3x
2
-12ax-5 is divided by x-1, the remainder R
1
and when the
polynomial 2x
3
+ax
2
-6x+2 is divided by x+2, the remainder R
2
. If 3R
1
+R
2
+28 = 0, find the
value of a.
71. Find the value of x
3
+ y
3
+ z
3
-3xyz if x
2
+ y
2
+z
2
= 83 and x+y+z=15
72. Assertion : is a quadratic polynomial.
๐ฆ
2
+ 4 ๐ฆ + 3
Reason: A degree of polynomial 2 is called quadratic polynomial.
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
73. Assertion: The value of
102 ( )
2
= 1061208
Reason:
๐ฅ + ๐ฆ ( )
3
= ๐ฅ
3
+ ๐ฆ
3
+ 3 ๐ฅ๐ฆ ( ๐ฅ + ๐ฆ )
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
74. Assertion:
2 ๐ฅ
2
โ ๐ฆ
2
+ ๐ง
2
โ 2 2 ๐ฅ๐ฆ โ 2 ๐ฆ๐ง + 2 2 ๐ง๐ฅ = 2 ๐ฅ โ ๐ฆ + ๐ง
( )
2
Reason: ๐
2
+ ๐
2
+ ๐
2
+ 2 ( ๐๐ + ๐๐ + ๐๐ )= ๐ + ๐ + ๐ ( )
2
a. Both assertion (A) and reason (R) are true and (R) is the correct explanation of
assertion (A).
b. Both assertion (A) and reason (R) are true and (R) is not the correct explanation
of assertion (A).
c. Assertion (A) is true but reason (R) is false.
d. Assertion (A) is false but reason (R) is true.
75. David, a student of class IX visited a book shop of his school to purchase the maths lab
kit. Mr Roy, who is running the bookshop in school told David that Maths lab kit consists
of a lab manual and a notebook and the total cost of lab kit is . He also told ๐ฅ
2
+ 6 ๐ฅ + 9
David that the total price of the kit includes the individual price of Manual and Notebook.
On the basis of above information answer the following question?
a. The price of kit is given by . What is the degree of the equation?
๐ฅ
2
+ 6 ๐ฅ + 9
b. is which type of polynomial.
๐ฅ
2
+ 6 ๐ฅ + 9
c. Find zero of polynomial .
๐ฅ
2
+ 6 ๐ฅ + 9
SMART EDUCATIONS
5 SMART EDUCATIONS ( www.smarteducations.org )
76. One day, the principal of a particular school visited the classroom. Class teacher was
teaching the concept of polynomials to students. He was very much impressed by her
way of teaching. To check whether the students also understand the concept taught by
her or not, he asked various questions to students. Some of them are given below.
Answer them.
a. Which one of the following is not a polynomial?
i. 4x
2
+2x-1
ii.
๐ฆ +
1
๐ฆ
iii. x
3
-1
iv. y
2
+5y+1
77. Ankur and Ranjan start a new business together. The amount invested by both partners
together is given by the polynomial , which is the product of their
๐ ( ๐ฅ )= 4 ๐ฅ
2
+ 12 ๐ฅ + 5
individual shares.
a. Coefficient of in the given polynomial is?
๐ฅ
2
b. Total amount invested by both, if x= 1000 is?
c. The shares of Ankur and Rajan invested individually are
d. What is the name given to the polynomial which represents the amount that each
of them has invested?
78. A school organised a mathematics exhibition in the school premises. A student made
two hangings related to polynomials which are shown in the figure,
Based on the given information given in the hanging, answer the following :
a. Find the value of p(5).
b. What are the factors of f(x)
c. Factorise: 9y
2
-9y +2
d. Find the length and breadth of the first hanging.
