EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factor Theorem
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If
1
is the zero of the polynomial
f
(
x
)
=
3
x
2
−
6
x
+
k
,
find
k
(i)
5
(ii)
0
(iii)
3
(iv)
2
(v)
4
Question
2
2.
The value of the polynomial
(
5
y
4
+
9
y
3
+
2
y
2
+
8
y
+
7
)
at
y
=
2
is
(i)
186
(ii)
183
(iii)
184
(iv)
181
(v)
182
Question
3
3.
If
f
(
x
)
=
(
2
x
3
−
5
x
2
−
6
x
+
9
)
and
g
(
x
)
=
(
x
3
+
x
2
−
9
x
−
9
)
have a common factor, find the common factor
(i)
(
2
x
+
3
)
(ii)
(
x
+
3
)
(iii)
(
x
−
1
)
(iv)
(
x
+
1
)
(v)
(
x
−
3
)
Question
4
4.
The degree of the polynomial
(
−
3
r
2
−
4
r
+
2
)
is
(i)
3
(ii)
2
(iii)
1
(iv)
0
(v)
5
Question
5
5.
If
1
and
-2
are the zeros of the polynomial
f
(
x
)
=
b
x
4
+
7
x
3
+
x
2
+
a
x
, find the value of
a
and
b
(i)
-10
,
3
(ii)
3
,
-9
(iii)
-9
,
2
(iv)
1
,
-11
(v)
-10
,
2
Question
6
6.
Given
f
(
p
)
=
(
−
p
2
−
8
p
+
3
)
,
find
f
(
4
)
(i)
-44
(ii)
-42
(iii)
-45
(iv)
-48
(v)
-46
Question
7
7.
Factorize
(
x
4
+
6
x
3
−
36
x
2
−
86
x
−
45
)
(i)
(
x
−
5
)
(
2
x
+
9
)
(
2
x
+
1
)
(
2
x
+
1
)
(ii)
(
x
−
5
)
9
1
1
(iii)
(
x
−
5
)
(
−
x
+
9
)
(
−
2
x
+
1
)
(
−
x
+
1
)
(iv)
(
x
−
5
)
(
x
+
9
)
(
x
+
1
)
(
x
+
1
)
(v)
(
x
−
5
)
(
4
x
+
9
)
(
4
x
+
1
)
(
3
x
+
1
)
Question
8
8.
(
−
16
x
4
+
24
x
3
+
8
x
2
−
24
x
+
8
)
÷
(
8
x
3
−
4
x
2
−
8
x
+
4
)
=
(i)
(
−
2
x
−
2
)
(ii)
(
−
2
x
+
2
)
(iii)
(
−
x
+
2
)
(iv)
(
2
x
+
2
)
(v)
(
−
3
x
+
2
)
Question
9
9.
(
x
4
+
11
x
3
+
38
x
2
+
40
x
)
÷
(
x
2
+
7
x
+
10
)
(i)
(
x
2
+
5
x
)
(ii)
(
x
2
+
3
x
)
(iii)
(
x
2
−
4
x
)
(iv)
(
−
x
2
+
4
x
)
(v)
(
x
2
+
4
x
)
Question
10
10.
Which of the following polynomials is not a multiple of
(
x
+
3
)
?
(i)
(
6
x
2
−
5
x
−
6
)
(ii)
(
3
x
2
+
13
x
+
12
)
(iii)
(
3
x
2
+
14
x
+
15
)
(iv)
(
3
x
2
+
11
x
+
6
)
(v)
(
2
x
2
+
3
x
−
9
)
Question
11
11.
The remainder when
(
−
f
4
+
6
f
3
−
9
f
2
+
4
f
+
5
)
is divided by
(
f
2
+
6
f
+
5
)
is
(i)
(
398
f
+
385
)
(ii)
(
400
f
+
385
)
(iii)
(
399
f
+
385
)
(iv)
(
403
f
+
385
)
(v)
(
401
f
+
385
)
Question
12
12.
Find the value of
a
and
b
such that
b
x
4
+
48
x
3
+
a
x
2
−
192
x
−
144
is exactly divisible by
(
4
x
2
−
2
x
−
12
)
(i)
-28
,
17
(ii)
15
,
-29
(iii)
-28
,
16
(iv)
-27
,
16
(v)
17
,
-27
Question
13
13.
The quotient when
(
9
y
−
3
)
is divided by
(
y
−
4
)
is
(i)
10
(ii)
7
(iii)
8
(iv)
9
(v)
12
Question
14
14.
Find the value of
k
such that
16
x
4
−
8
x
3
−
100
x
2
+
k
x
+
60
is exactly divisible by
(
2
x
−
4
)
(i)
72
(ii)
77
(iii)
73
(iv)
75
(v)
74
Question
15
15.
Factorize
(
x
2
+
2
x
a
+
x
+
a
2
+
a
−
30
)
(i)
(
x
+
a
−
5
)
(
x
−
a
+
6
)
(ii)
(
x
−
a
+
6
)
(
x
+
a
+
5
)
(iii)
(
x
+
a
+
6
)
(
x
+
a
−
5
)
(iv)
(
x
+
a
+
6
)
(
x
−
a
−
5
)
(v)
(
x
−
a
−
5
)
(
x
+
a
−
6
)
Question
16
16.
Factorize
(
6
x
2
+
20
x
+
16
)
(i)
(
2
x
+
4
)
(
5
x
+
4
)
(ii)
(
2
x
+
4
)
(
4
x
+
4
)
(iii)
(
2
x
+
4
)
(
2
x
+
4
)
(iv)
(
2
x
+
4
)
(
3
x
+
4
)
(v)
(
2
x
+
4
)
4
Question
17
17.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
−
36
x
2
−
60
x
−
25
)
(i)
(
6
x
−
5
)
(
−
6
x
+
5
)
(ii)
(
6
x
−
5
)
(
−
6
x
−
5
)
(iii)
(
−
6
x
−
3
)
(
−
6
x
+
5
)
(iv)
(
6
x
+
5
)
(
−
6
x
−
5
)
(v)
(
6
x
+
5
)
(
−
6
x
+
5
)
Question
18
18.
The remainder when
(
−
8
x
3
+
9
x
2
+
3
x
)
is divided by
(
x
+
7
)
is
(i)
3165
(ii)
3161
(iii)
3166
(iv)
3163
(v)
3164
Question
19
19.
If one of the roots of the cubic equation
(
98
x
3
−
413
x
2
+
484
x
−
160
)
=
0
is
5
2
,
find the remaining real roots
(i)
(
3
2
,
2
7
)
(ii)
(
4
7
,
8
7
)
(iii)
(
7
2
,
6
7
)
(iv)
(
3
,
4
5
)
(v)
(
9
4
,
4
9
)
Question
20
20.
The quotient when
(
5
n
2
+
7
n
−
3
)
is divided by
(
n
−
7
)
is
(i)
(
3
n
+
42
)
(ii)
(
4
n
+
42
)
(iii)
(
6
n
+
42
)
(iv)
(
8
n
+
42
)
(v)
(
5
n
+
42
)
Question
21
21.
(
4
x
3
−
4
x
2
−
20
x
−
12
)
÷
(
2
x
2
−
4
x
−
6
)
=
(i)
(
3
x
+
2
)
(ii)
(
−
2
x
+
2
)
(iii)
(
2
x
−
2
)
(iv)
(
2
x
+
2
)
(v)
(
x
+
2
)
Question
22
22.
The quotient when
4
p
is divided by
6
is
(i)
2
5
p
(ii)
2
p
(iii)
2
3
p
(iv)
4
3
p
(v)
0
Question
23
23.
The quotient when
(
−
g
4
+
5
g
3
+
7
g
2
−
5
g
+
8
)
is divided by
(
g
2
+
5
g
−
36
)
is
(i)
(
−
3
g
2
+
10
g
−
79
)
(ii)
(
−
g
2
+
10
g
−
79
)
(iii)
(
−
2
g
2
+
10
g
−
79
)
(iv)
(
10
g
−
79
)
(v)
(
2
g
2
+
10
g
−
79
)
Question
24
24.
Given
f
(
u
)
=
(
7
u
3
+
2
u
2
−
5
)
,
find
f
(
(-3)
)
(i)
-179
(ii)
-173
(iii)
-177
(iv)
-175
(v)
-176
Question
25
25.
(
4
x
3
+
x
2
)
÷
x
(i)
(
−
4
x
2
+
x
)
(ii)
(
4
x
2
+
2
x
)
(iii)
(
4
x
2
−
x
)
(iv)
(
4
x
2
+
x
)
(v)
(
3
x
2
+
x
)
Assignment Key
1) (iii)
2) (ii)
3) (v)
4) (ii)
5) (v)
6) (iii)
7) (iv)
8) (ii)
9) (v)
10) (i)
11) (ii)
12) (iii)
13) (iv)
14) (v)
15) (iii)
16) (iv)
17) (iv)
18) (v)
19) (ii)
20) (v)
21) (iv)
22) (iii)
23) (ii)
24) (v)
25) (iv)
