EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
Find the value of
a
and
b
such that
a
x
4
+
12
x
3
−
28
x
2
−
60
x
+
b
is exactly divisible by
(
2
x
2
+
2
x
−
12
)
(i)
4
,
72
(ii)
71
,
3
(iii)
5
,
72
(iv)
73
,
5
(v)
4
,
73
Question
2
2.
The degree of the polynomial
(
−
9
k
2
−
k
−
4
)
is
(i)
5
(ii)
0
(iii)
2
(iv)
3
(v)
1
Question
3
3.
Which of the following algebraic expressions is a constant polynomial?
(i)
(
−
4
)
(ii)
(
−
6
g
2
h
i
2
−
4
g
2
h
−
3
g
i
3
+
9
g
i
2
)
(iii)
(
−
3
g
2
−
2
i
3
−
2
)
(iv)
7
g
h
3
i
(v)
(
−
4
g
3
h
i
−
6
g
2
h
2
i
2
)
Question
4
4.
The quotient of
(
−
125
a
3
+
375
a
2
b
−
375
a
b
2
+
125
b
3
)
÷
(
−
5
a
+
5
b
)
is
(i)
(
25
a
2
−
50
a
b
+
25
b
2
)
(ii)
(
25
a
2
−
53
a
b
+
25
b
2
)
(iii)
(
26
a
2
−
50
a
b
+
25
b
2
)
(iv)
(
25
a
2
−
48
a
b
+
25
b
2
)
(v)
(
24
a
2
−
50
a
b
+
25
b
2
)
Question
5
5.
Which of the following are true?
a)
Degree of zero polynomial is zero
b)
π
r
2
is a monomial
c)
Every polynomial is a binomial
d)
A binomial has two and only two terms
e)
A binomial may have degree 3
(i)
{c,d}
(ii)
{a,b}
(iii)
{b,d,e}
(iv)
{a,c,e}
(v)
{a,b,d}
Question
6
6.
The remainder when
6
j
2
is divided by
(
j
−
7
)
is
(i)
295
(ii)
292
(iii)
293
(iv)
294
(v)
296
Question
7
7.
The quotient of
(
16
a
2
−
b
2
)
÷
(
4
a
+
b
)
is
(i)
(
3
a
−
b
)
(ii)
(
5
a
−
b
)
(iii)
(
4
a
−
b
)
(iv)
(
4
a
+
2
b
)
(v)
(
4
a
−
3
b
)
Question
8
8.
Factorize
(
x
2
+
2
x
a
+
2
x
+
a
2
+
2
a
−
8
)
(i)
(
x
+
a
+
4
)
(
x
+
a
−
2
)
(ii)
(
x
+
a
−
2
)
(
x
−
a
+
4
)
(iii)
(
x
+
a
+
4
)
(
x
−
a
−
2
)
(iv)
(
x
−
a
+
4
)
(
x
+
a
+
2
)
(v)
(
x
−
a
−
2
)
(
x
+
a
−
4
)
Question
9
9.
Which of the following polynomials is not a multiple of
(
3
x
−
2
)
?
(i)
(
3
x
2
+
x
−
2
)
(ii)
(
3
x
2
+
7
x
−
6
)
(iii)
(
3
x
2
+
4
x
+
1
)
(iv)
(
3
x
2
+
4
x
−
4
)
(v)
(
9
x
2
−
3
x
−
2
)
Question
10
10.
The value of
35
✕
25
is
(i)
873
(ii)
874
(iii)
875
(iv)
876
(v)
877
Question
11
11.
Which of the following polynomials has
(
x
−
3
)
as a factor ?
(i)
(
12
x
3
+
22
x
2
−
2
x
−
12
)
(ii)
(
18
x
3
−
81
x
2
+
106
x
−
40
)
(iii)
(
12
x
3
−
28
x
2
−
29
x
+
60
)
(iv)
(
8
x
3
−
38
x
−
30
)
(v)
(
6
x
3
−
16
x
2
−
10
x
+
12
)
Question
12
12.
Which of the following are not polynomials?
a)
(
2
x
+
11
y
)
b)
√x
c)
(
8
x
−
4
y
)
d)
64
x
2
e)
64
x
2
+
1
64
x
2
(i)
{c,e,b}
(ii)
{c,e}
(iii)
{b,e}
(iv)
{a,b}
(v)
{d,a,b}
Question
13
13.
The remainder when
(
9
b
+
1
)
is divided by
(
b
−
4
)
is
(i)
37
(ii)
39
(iii)
36
(iv)
38
(v)
34
Question
14
14.
The expanded form of
(
x
−
6
)
(
2
x
+
3
)
(
2
x
+
6
)
is
(i)
(
5
x
3
−
6
x
2
−
90
x
−
108
)
(ii)
(
6
x
3
−
6
x
2
−
90
x
−
108
)
(iii)
(
3
x
3
−
6
x
2
−
90
x
−
108
)
(iv)
(
4
x
3
−
6
x
2
−
90
x
−
108
)
(v)
(
2
x
3
−
6
x
2
−
90
x
−
108
)
Question
15
15.
(
4
x
4
y
4
z
2
+
36
x
4
y
3
z
2
+
12
x
3
y
4
z
3
)
÷
2
x
2
y
2
z
=
(i)
(
18
x
2
y
2
z
2
+
2
x
2
y
2
z
+
6
x
y
2
z
2
)
(ii)
(
2
x
3
y
4
z
+
18
x
2
y
z
+
6
x
y
2
z
2
)
(iii)
(
2
x
3
y
3
z
+
18
x
2
y
z
+
6
x
y
2
z
2
)
(iv)
(
2
x
2
y
2
z
+
6
x
y
2
z
2
+
18
x
y
2
z
)
(v)
(
2
x
2
y
2
z
+
18
x
2
y
z
+
6
x
y
2
z
2
)
Question
16
16.
Given
f
(
m
)
=
(
−
3
m
−
9
)
,
find
f
(
(-2)
)
(i)
-4
(ii)
0
(iii)
-2
(iv)
-6
(v)
-3
Question
17
17.
The coefficient of term
o
p
in polynomial
(
−
o
p
−
5
o
−
8
p
+
4
)
is
(i)
0
(ii)
-2
(iii)
1
(iv)
-3
(v)
-1
Question
18
18.
The constant term in polynomial
(
−
4
r
2
+
9
r
−
7
)
is
(i)
-8
(ii)
-7
(iii)
-10
(iv)
-4
(v)
-6
Question
19
19.
Factorize
(
20
a
2
b
+
35
a
b
2
)
(i)
5
a
b
(
−
4
a
−
7
b
)
(ii)
5
b
(
4
a
−
7
b
)
(iii)
5
a
b
(
4
a
+
7
b
)
(iv)
5
a
(
4
a
+
7
b
)
(v)
5
a
b
(
4
a
−
7
b
)
Question
20
20.
The quotient of
(
16
a
2
−
8
a
b
+
b
2
)
÷
(
−
4
a
+
b
)
is
(i)
(
−
4
a
+
b
)
(ii)
(
−
3
a
+
b
)
(iii)
(
−
4
a
+
4
b
)
(iv)
(
−
5
a
+
b
)
(v)
(
−
4
a
−
2
b
)
Question
21
21.
Factorize
(
a
x
+
b
y
)
2
−
(
a
x
−
b
y
)
2
(i)
4
(
a
x
)
2
(
b
y
)
2
(ii)
2
(
a
x
)
2
(
b
y
)
2
(iii)
4
a
x
b
y
(iv)
2
a
x
b
y
Question
22
22.
Find the value of
60
3
+
25
3
−
85
3
(i)
(-125000)
(ii)
(-1728000)
(iii)
125000
(iv)
1728000
(v)
(-382500)
Question
23
23.
The degree of polynomial
(
−
4
t
2
v
2
+
6
t
u
+
8
t
−
9
u
2
−
5
)
is
(i)
5
(ii)
3
(iii)
6
(iv)
4
(v)
2
Question
24
24.
(
a
+
b
+
c
)
2
(i)
(
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(ii)
(
a
2
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iii)
(
a
2
+
5
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iv)
(
2
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(v)
(
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
Question
25
25.
The degree of polynomial
(
2
t
u
−
8
t
−
7
u
−
1
)
is
(i)
1
(ii)
2
(iii)
3
(iv)
(-1)
(v)
4
Assignment Key
1) (i)
2) (iii)
3) (i)
4) (i)
5) (iii)
6) (iv)
7) (iii)
8) (i)
9) (iii)
10) (iii)
11) (v)
12) (iii)
13) (i)
14) (iv)
15) (v)
16) (v)
17) (v)
18) (ii)
19) (iii)
20) (i)
21) (iii)
22) (v)
23) (iv)
24) (v)
25) (ii)
