EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factor Theorem
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The quotient when
4
h
is divided by
3
is
(i)
4
3
h
(ii)
2
h
(iii)
6
5
h
(iv)
2
3
h
Question
2
2.
If one of the roots of the cubic equation
(
x
3
+
3
x
2
−
33
x
−
35
)
=
0
is
(
−
7
)
,
find the remaining real roots
(i)
(
(
−
9
)
,
2
)
(ii)
(
(
−
4
)
,
8
)
(iii)
(
(
−
8
)
,
4
)
(iv)
(
(
−
6
)
,
6
)
(v)
(
5
,
(
−
1
)
)
Question
3
3.
Which of the following polynomials has
(
3
x
−
5
)
as a factor ?
(i)
(
18
x
3
+
24
x
2
+
2
x
−
4
)
(ii)
(
6
x
3
+
22
x
2
−
38
x
+
10
)
(iii)
(
6
x
3
+
28
x
2
−
14
x
−
20
)
(iv)
(
12
x
3
+
8
x
2
−
12
x
−
8
)
(v)
(
9
x
3
+
27
x
2
−
85
x
+
25
)
Question
4
4.
Find the value of
a
and
b
such that
4
x
4
+
a
x
3
+
b
x
2
−
25
x
+
500
is exactly divisible by
(
x
2
+
x
−
20
)
(i)
4
,
-105
(ii)
-106
,
3
(iii)
5
,
-105
(iv)
-104
,
5
(v)
4
,
-104
Question
5
5.
The remainder when
6
n
2
is divided by
(
n
+
3
)
is
(i)
54
(ii)
55
(iii)
51
(iv)
56
(v)
53
Question
6
6.
If
2
3
is the zero of the polynomial
f
(
x
)
=
9
x
2
+
k
,
find
k
(i)
-7
(ii)
-4
(iii)
-2
(iv)
-5
(v)
-3
Question
7
7.
The degree of the polynomial
(
6
r
5
−
7
r
4
−
7
r
3
−
9
r
2
−
r
)
is
(i)
8
(ii)
4
(iii)
5
(iv)
6
(v)
3
Question
8
8.
Which of the following are true ?
a)
If the degree of p(x) is less then the degree of d(x), we should not divide p(x) with d(x)
b)
If p(a) = 0, then (x + a) perfectly divides p(x)
c)
If p(x) is divided by (x - a), the remainder is p(a)
d)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
(i)
{b,c,a}
(ii)
{a,c}
(iii)
{b,a}
(iv)
{b,d,a}
(v)
{d,c}
Question
9
9.
The degree of the polynomial
(
d
3
+
2
d
−
2
)
is
(i)
3
(ii)
0
(iii)
6
(iv)
4
(v)
2
Question
10
10.
Given
f
(
n
)
=
(
−
4
n
+
1
)
,
find
f
(
0
)
(i)
0
(ii)
1
(iii)
4
(iv)
2
(v)
-1
Question
11
11.
Which of the following are true?
a)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
b)
If (x - a) is a factor of f(x), then f(a) = 0
c)
If (x + a) is a factor of f(x), then f(a) = 0
d)
A polynomial of degree n has atmost n zeros
e)
Zero of a polynomial and zero polynomial are synonymous
f)
Zero of a polynomial and root of the polynomial are synonymous
g)
A linear polynomial in one variable has only one root
(i)
{c,f,g}
(ii)
{a,b,d,f,g}
(iii)
{c,a}
(iv)
{c,e,d}
(v)
{e,b}
Question
12
12.
(
15
x
3
+
15
x
2
)
÷
5
x
(i)
(
3
x
2
−
3
x
)
(ii)
(
3
x
2
+
4
x
)
(iii)
(
3
x
2
+
3
x
)
(iv)
(
2
x
2
+
3
x
)
(v)
(
−
3
x
2
+
3
x
)
Question
13
13.
(
18
x
5
−
48
x
4
−
48
x
3
+
84
x
2
+
30
x
−
36
)
divided by
(
18
x
3
+
24
x
2
−
6
x
−
12
)
=
(i)
(
x
2
−
4
x
−
3
)
(ii)
(
x
2
−
3
x
+
3
)
(iii)
(
x
2
+
4
x
+
3
)
(iv)
(
x
2
−
5
x
+
3
)
(v)
(
x
2
−
4
x
+
3
)
Question
14
14.
The value of the polynomial
(
6
f
2
−
9
f
+
3
)
at
f
=
(-4)
is
(i)
138
(ii)
134
(iii)
132
(iv)
136
(v)
135
Question
15
15.
The quotient when
(
6
t
2
+
4
t
−
3
)
is divided by
(
t
+
8
)
is
(i)
(
6
t
−
44
)
(ii)
(
5
t
−
44
)
(iii)
(
4
t
−
44
)
(iv)
(
7
t
−
44
)
(v)
(
8
t
−
44
)
Question
16
16.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
12
x
2
+
22
x
+
10
)
(i)
(
−
2
x
+
2
)
(
−
6
x
+
5
)
(ii)
(
−
2
x
+
2
)
(
−
6
x
−
5
)
(iii)
(
−
2
x
−
2
)
(
−
6
x
−
5
)
(iv)
(
−
2
x
−
2
)
(
−
6
x
+
5
)
(v)
(
−
4
x
+
2
)
(
−
6
x
+
5
)
Question
17
17.
Which of the following polynomials is not a multiple of
(
x
−
2
)
?
(i)
(
x
2
−
x
−
2
)
(ii)
(
x
2
−
4
)
(iii)
(
2
x
2
−
5
x
+
2
)
(iv)
(
2
x
2
+
x
−
1
)
(v)
(
x
2
+
3
x
−
10
)
Question
18
18.
Find the value of
k
such that
8
x
4
−
16
x
3
−
110
x
2
+
k
x
is exactly divisible by
(
2
x
+
5
)
(i)
-49
(ii)
-48
(iii)
-51
(iv)
-53
(v)
-50
Question
19
19.
Which of the following polynomials is a multiple of
(
x
+
4
)
?
(i)
(
12
x
3
−
16
x
2
−
27
x
+
36
)
(ii)
(
4
x
3
−
19
x
+
15
)
(iii)
(
6
x
3
+
x
2
−
27
x
+
20
)
(iv)
(
8
x
3
+
20
x
2
−
18
x
−
45
)
(v)
(
3
x
3
+
5
x
2
−
24
x
+
16
)
Question
20
20.
The degree of the polynomial
(
−
7
g
2
−
9
g
−
4
)
is
(i)
2
(ii)
3
(iii)
4
(iv)
0
(v)
1
Question
21
21.
Factorize
(
4
x
3
+
28
x
2
−
11
x
−
210
)
(i)
(
x
+
6
)
(
−
x
−
5
)
(
−
x
+
7
)
(ii)
(
x
+
6
)
(
2
x
−
5
)
(
2
x
+
7
)
(iii)
(
x
+
6
)
(
3
x
−
5
)
(
3
x
+
7
)
(iv)
(
x
+
6
)
(
4
x
−
5
)
(
5
x
+
7
)
(v)
(
x
+
6
)
(
x
−
5
)
(
x
+
7
)
Question
22
22.
The quotient when
(
6
b
5
+
2
b
4
−
3
b
3
−
5
b
2
+
7
b
−
8
)
is divided by
(
b
+
6
)
is
(i)
(
6
b
4
−
34
b
3
+
201
b
2
−
1211
b
+
7273
)
(ii)
(
4
b
4
−
34
b
3
+
201
b
2
−
1211
b
+
7273
)
(iii)
(
5
b
4
−
34
b
3
+
201
b
2
−
1211
b
+
7273
)
(iv)
(
7
b
4
−
34
b
3
+
201
b
2
−
1211
b
+
7273
)
(v)
(
9
b
4
−
34
b
3
+
201
b
2
−
1211
b
+
7273
)
Question
23
23.
(
324
x
4
y
3
+
36
x
3
y
4
)
÷
6
x
2
y
2
=
(i)
(
54
x
2
y
+
6
x
y
2
)
(ii)
(
54
x
2
y
+
6
y
3
)
(iii)
(
54
x
2
y
+
6
x
y
3
z
)
(iv)
(
54
x
3
y
3
+
6
x
y
2
)
(v)
(
54
x
3
y
2
+
6
x
y
2
)
Question
24
24.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
6
x
+
12
,
find the value of
a
(i)
0
(ii)
(-1)
(iii)
(-3)
(iv)
(-2)
(v)
(-5)
Question
25
25.
If the polynomial
b
x
4
+
a
x
3
−
25
x
2
+
37
x
+
60
is divided by
(
x
−
2
)
,
it leaves a remainder
42
.
If it is divided by
(
x
−
3
)
,
it leaves a remainder
0
.
Find the value of
a
and
b
(i)
-1
,
2
(ii)
0
,
1
(iii)
2
,
0
(iv)
-1
,
1
(v)
0
,
-2
Assignment Key
1) (i)
2) (v)
3) (v)
4) (i)
5) (i)
6) (ii)
7) (iii)
8) (ii)
9) (i)
10) (ii)
11) (ii)
12) (iii)
13) (v)
14) (v)
15) (i)
16) (iii)
17) (iv)
18) (v)
19) (v)
20) (i)
21) (ii)
22) (i)
23) (i)
24) (iv)
25) (iv)
