EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials and Factorisation
Grade : SSC Grade IX
License : Non Commercial Use
Question
1
1.
The expanded form of
(
3
x
−
1
)
(
2
x
+
3
)
(
3
x
−
4
)
is
(i)
(
17
x
3
−
3
x
2
−
37
x
+
12
)
(ii)
(
18
x
3
−
3
x
2
−
37
x
+
12
)
(iii)
(
19
x
3
−
3
x
2
−
37
x
+
12
)
(iv)
(
15
x
3
−
3
x
2
−
37
x
+
12
)
(v)
(
21
x
3
−
3
x
2
−
37
x
+
12
)
Question
2
2.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
−
x
3
−
5
x
2
+
9
x
+
45
)
,
g
(
x
)
=
(
x
+
3
)
(ii)
f
(
x
)
=
(
x
3
−
2
x
2
−
16
x
+
32
)
,
g
(
x
)
=
(
−
x
+
3
)
(iii)
f
(
x
)
=
(
−
x
3
−
7
x
2
−
2
x
+
40
)
,
g
(
x
)
=
(
−
x
+
4
)
(iv)
f
(
x
)
=
(
x
3
+
12
x
2
+
47
x
+
60
)
,
g
(
x
)
=
(
−
x
+
2
)
(v)
f
(
x
)
=
(
x
3
−
x
2
−
14
x
+
24
)
,
g
(
x
)
=
(
x
+
5
)
Question
3
3.
Expand
(
x
+
1
x
)
2
(i)
x
2
+
2
+
1
x
2
(ii)
x
3
+
2
+
1
x
2
(iii)
x
2
+
2
−
1
x
2
(iv)
x
2
+
2
+
1
x
3
(v)
x
2
+
2
+
4
x
2
Question
4
4.
The degree of polynomial
(
−
w
x
−
3
w
−
x
+
4
)
is
(i)
3
(ii)
5
(iii)
(-1)
(iv)
2
(v)
1
Question
5
5.
The value of the polynomial
(
5
p
r
+
2
q
r
+
3
q
)
at
p
=
(-5)
,
q
=
4
,
r
=
(-5)
is
(i)
99
(ii)
97
(iii)
96
(iv)
98
(v)
95
Question
6
6.
The remainder when
(
−
r
4
+
8
r
3
−
9
r
2
+
4
r
−
8
)
is divided by
(
r
2
−
2
r
−
63
)
is
(i)
(
262
r
−
3788
)
(ii)
(
261
r
−
3788
)
(iii)
(
259
r
−
3788
)
(iv)
(
265
r
−
3788
)
(v)
(
263
r
−
3788
)
Question
7
7.
Which of the following algebraic expressions is a linear polynomial?
(i)
(
−
e
5
−
4
e
4
−
8
e
3
−
4
e
−
7
)
(ii)
(
e
3
+
9
e
2
−
e
+
7
)
(iii)
(
−
8
)
(iv)
(
5
e
2
−
2
e
+
9
)
(v)
(
−
2
e
−
8
)
Question
8
8.
The quotient of
(
4
a
2
+
20
a
b
−
4
a
c
+
25
b
2
−
10
b
c
+
c
2
)
÷
(
2
a
+
5
b
−
c
)
is
(i)
(
2
a
+
5
b
−
c
)
(ii)
(
3
a
+
5
b
−
c
)
(iii)
(
2
a
+
2
b
−
c
)
(iv)
(
2
a
+
7
b
−
c
)
(v)
(
a
+
5
b
−
c
)
Question
9
9.
The value of the polynomial
6
m
2
n
at
l
=
3
,
m
=
3
,
n
=
(-2)
is
(i)
-107
(ii)
-105
(iii)
-110
(iv)
-108
(v)
-109
Question
10
10.
The value of the polynomial
(
8
j
2
k
l
2
−
6
j
k
2
+
7
)
at
j
=
(-3)
,
k
=
4
,
l
=
0
is
(i)
294
(ii)
297
(iii)
292
(iv)
295
(v)
296
Question
11
11.
The degree of polynomial
(
−
w
3
x
3
y
−
6
w
3
+
6
w
2
x
−
6
w
2
y
2
−
6
x
2
+
7
x
y
+
2
y
3
)
is
(i)
8
(ii)
7
(iii)
5
(iv)
6
(v)
9
Question
12
12.
If
(
a
+
b
)
=
7
,
a
b
=
12
, find
(
a
2
+
b
2
)
(i)
24
(ii)
26
(iii)
25
(iv)
27
(v)
22
Question
13
13.
Factorize
(
2
a
−
5
b
)
3
+
(
5
b
−
4
c
)
3
+
(
4
c
−
2
a
)
3
(i)
3
(
2
a
−
5
b
)
(
5
b
−
4
c
)
(
4
c
−
2
a
)
(ii)
3
(
2
a
−
5
b
)
(
5
b
+
4
c
)
(
4
c
−
2
a
)
(iii)
3
(
2
a
−
5
b
)
(
5
b
+
4
c
)
(
4
c
+
2
a
)
(iv)
3
(
2
a
−
5
b
)
(
5
b
−
4
c
)
(
4
c
+
2
a
)
(v)
3
(
2
a
+
5
b
)
(
5
b
−
4
c
)
(
4
c
−
2
a
)
Question
14
14.
(
3
2
a
−
3
2
b
)
(
9
4
a
2
+
9
4
a
b
+
9
4
b
2
)
(i)
(
33
10
a
3
−
27
8
b
3
)
(ii)
(
27
8
a
3
−
29
8
b
3
)
(iii)
(
27
8
a
3
−
25
8
b
3
)
(iv)
(
7
2
a
3
−
27
8
b
3
)
(v)
(
27
8
a
3
−
27
8
b
3
)
Question
15
15.
Which of the following terms can be subtracted from
9
x
2
y
w
2
?
(i)
(
−
2
w
x
y
)
(ii)
4
w
x
2
y
(iii)
7
w
2
x
2
y
(iv)
9
w
2
x
y
(v)
8
w
2
x
y
2
Question
16
16.
The coefficient of term
p
q
in polynomial
(
6
p
q
+
2
p
−
15
q
+
4
)
is
(i)
6
(ii)
3
(iii)
7
(iv)
5
(v)
9
Question
17
17.
Factorize
(
64
a
3
−
144
a
2
b
+
108
a
b
2
−
27
b
3
)
(i)
(
4
a
−
3
b
)
(
4
a
−
3
b
)
(
4
a
−
3
b
)
(ii)
(
5
a
−
3
b
)
(
5
a
−
3
b
)
(
5
a
−
3
b
)
(iii)
(
4
a
−
b
)
(
4
a
−
b
)
(
4
a
−
b
)
(iv)
(
3
a
−
3
b
)
(
3
a
−
3
b
)
(
3
a
−
3
b
)
(v)
(
4
a
−
5
b
)
(
4
a
−
6
b
)
(
4
a
−
5
b
)
Question
18
18.
If the polynomials
3
x
2
+
a
x
−
19
and
a
x
2
+
4
x
−
5
leave the same remainder when divided by
(
x
+
2
)
,
find the value of
a
(i)
(-1)
(ii)
0
(iii)
4
(iv)
1
(v)
2
Question
19
19.
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
(i)
(
a
3
−
2
b
3
)
(ii)
b
3
(iii)
(
a
3
+
3
b
3
)
(iv)
(
2
a
3
+
b
3
)
(v)
(
a
3
+
b
3
)
Question
20
20.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
12
x
2
−
24
x
+
12
)
(i)
(
−
4
x
+
4
)
(
−
3
x
−
3
)
(ii)
(
−
4
x
−
4
)
(
−
3
x
+
3
)
(iii)
(
−
4
x
−
4
)
(
−
3
x
−
3
)
(iv)
(
−
4
x
+
4
)
(
−
3
x
+
3
)
(v)
(
−
4
x
+
1
)
(
−
3
x
−
3
)
Question
21
21.
Factorize
(
18
x
2
+
62
x
y
+
24
y
2
)
(i)
(
2
x
−
6
y
)
(
9
x
+
4
y
)
(ii)
(
2
x
+
6
y
)
(
2
x
−
6
y
)
(iii)
(
2
x
−
6
y
)
(
9
x
−
4
y
)
(iv)
(
2
x
+
6
y
)
(
9
x
−
4
y
)
(v)
(
2
x
+
6
y
)
(
9
x
+
4
y
)
Question
22
22.
The value of
899
3
4
✕
899
3
4
is
(i)
809550
1
14
(ii)
809550
1
16
(iii)
809550
1
18
(iv)
809549
15
16
(v)
809550
3
16
Question
23
23.
Given
f
(
t
)
=
(
8
t
4
−
6
t
3
+
2
t
2
−
5
t
−
1
)
,
find
f
(
(-1)
)
(i)
17
(ii)
19
(iii)
21
(iv)
23
(v)
20
Question
24
24.
The value of the polynomial
(
−
9
n
2
o
2
p
−
5
n
2
o
−
3
n
o
2
)
at
n
=
(-4)
,
o
=
(-4)
,
p
=
0
is
(i)
512
(ii)
515
(iii)
509
(iv)
511
(v)
513
Question
25
25.
Evaluate :
980
2
−
20
2
(i)
9600000
(ii)
960000
(iii)
960020
(iv)
960980
(v)
96000
Assignment Key
1) (ii)
2) (i)
3) (i)
4) (iv)
5) (ii)
6) (i)
7) (v)
8) (i)
9) (iv)
10) (iv)
11) (ii)
12) (iii)
13) (i)
14) (v)
15) (iii)
16) (i)
17) (i)
18) (iv)
19) (v)
20) (iv)
21) (v)
22) (ii)
23) (v)
24) (i)
25) (ii)
