EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factor Theorem
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If
(
x
2
−
1
)
is a factor of
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
,
which of the following are true ?
a)
a + b + c = 0
b)
a + b + c + d + e = 0
c)
a + c + e = 0
d)
a + b + c = d + e
e)
b + d = 0
f)
d + e = 0
(i)
{d,c}
(ii)
{f,a,e}
(iii)
{b,c,e}
(iv)
{d,b,c}
(v)
{a,b}
Question
2
2.
(
36
x
4
y
4
+
4
x
4
y
3
)
÷
2
x
2
y
2
=
(i)
(
2
x
2
y
2
z
+
18
x
2
y
2
)
(ii)
(
18
x
2
y
2
+
2
x
y
2
)
(iii)
(
18
x
2
y
2
+
2
x
2
y
)
(iv)
(
18
x
3
y
4
+
2
x
2
y
)
(v)
(
18
x
3
y
3
+
2
x
2
y
)
Question
3
3.
Given
f
(
k
)
=
(
−
7
k
2
+
9
k
−
8
)
,
find
f
(
1
)
(i)
-8
(ii)
-6
(iii)
-3
(iv)
-7
(v)
-5
Question
4
4.
If one of the roots of the cubic equation
(
216
x
3
−
546
x
2
+
373
x
−
35
)
=
0
is
1
9
,
find the remaining real roots
(i)
(
(
−
1
9
)
,
5
6
)
(ii)
(
7
6
,
5
4
)
(iii)
(
1
11
,
9
8
)
(iv)
(
1
7
,
5
4
)
(v)
(
1
3
,
3
2
)
Question
5
5.
Find the value of
a
and
b
such that
a
x
4
−
5
x
3
−
19
x
2
+
125
x
+
b
is exactly divisible by
(
x
2
−
25
)
(i)
-151
,
0
(ii)
1
,
-149
(iii)
-149
,
2
(iv)
1
,
-150
(v)
2
,
-150
Question
6
6.
The value of the polynomial
(
−
9
n
4
+
n
3
−
4
n
2
+
9
n
−
3
)
at
n
=
(-2)
is
(i)
-189
(ii)
-192
(iii)
-190
(iv)
-186
(v)
-188
Question
7
7.
The degree of the polynomial
(
−
9
f
2
+
8
f
+
6
)
is
(i)
2
(ii)
5
(iii)
3
(iv)
1
(v)
(-1)
Question
8
8.
The quotient when
(
2
z
2
+
z
−
4
)
is divided by
(
z
+
4
)
is
(i)
(
z
−
7
)
(ii)
(
−
7
)
(iii)
(
5
z
−
7
)
(iv)
(
3
z
−
7
)
(v)
(
2
z
−
7
)
Question
9
9.
The quotient when
2
m
is divided by
(
−
6
)
is
(i)
(
−
m
)
(ii)
(
−
1
5
m
)
(iii)
1
3
m
(iv)
(
−
1
3
m
)
Question
10
10.
The quotient when
(
2
g
3
−
5
g
2
−
g
)
is divided by
(
g
2
−
15
g
+
56
)
is
(i)
(
g
+
25
)
(ii)
(
2
g
+
25
)
(iii)
(
4
g
+
25
)
(iv)
(
3
g
+
25
)
(v)
(
−
g
+
25
)
Question
11
11.
The quotient when
(
−
3
p
2
)
is divided by
(
p
−
4
)
is
(i)
(
−
4
p
−
12
)
(ii)
(
−
5
p
−
12
)
(iii)
(
−
3
p
−
12
)
(iv)
(
−
p
−
12
)
(v)
(
−
2
p
−
12
)
Question
12
12.
Factorize
(
x
3
+
3
x
2
a
+
3
x
a
2
−
x
+
a
3
−
a
)
(i)
(
x
−
a
)
(
x
−
a
−
1
)
(
x
+
a
+
1
)
(ii)
(
x
+
a
)
(
x
+
a
−
1
)
(
x
+
a
+
1
)
(iii)
(
x
−
a
)
(
x
+
a
−
1
)
(
x
−
a
+
1
)
(iv)
(
x
+
a
)
(
x
+
a
−
1
)
(
x
−
a
+
1
)
(v)
(
x
+
a
)
(
x
−
a
−
1
)
(
x
+
a
+
1
)
Question
13
13.
Which of the following are true ?
a)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
b)
If the degree of p(x) is less then the degree of d(x), we should not divide p(x) with d(x)
c)
If p(a) = 0, then (x + a) perfectly divides p(x)
d)
If p(x) is divided by (x - a), the remainder is p(a)
(i)
{a,b}
(ii)
{c,d}
(iii)
{b,d}
(iv)
{a,c,b}
(v)
{a,d,b}
Question
14
14.
(
3
x
3
+
8
x
2
+
3
x
−
2
)
÷
(
3
x
2
+
2
x
−
1
)
=
(i)
(
x
+
2
)
(ii)
(
x
−
2
)
(iii)
(
−
x
+
2
)
(iv)
(
2
x
+
2
)
(v)
2
Question
15
15.
The remainder when
(
−
8
c
−
9
)
is divided by
(
c
+
9
)
is
(i)
65
(ii)
63
(iii)
62
(iv)
64
(v)
60
Question
16
16.
The remainder when
(
−
7
i
3
−
4
i
2
+
4
i
)
is divided by
(
i
2
+
11
i
+
18
)
is
(i)
(
−
675
i
−
1314
)
(ii)
(
−
672
i
−
1314
)
(iii)
(
−
671
i
−
1314
)
(iv)
(
−
674
i
−
1314
)
(v)
(
−
673
i
−
1314
)
Question
17
17.
If the polynomial
f
(
x
)
=
2
x
2
−
2
x
+
k
is exactly divisible by
(
2
x
−
4
)
,
find
k
(i)
-2
(ii)
-7
(iii)
-5
(iv)
-4
(v)
-3
Question
18
18.
Which of the following polynomials has
(
2
x
+
1
)
as a factor ?
(i)
(
3
x
3
−
8
x
2
−
55
x
+
100
)
(ii)
(
x
3
+
4
x
2
−
25
x
−
100
)
(iii)
(
6
x
3
+
17
x
2
−
33
x
−
20
)
(iv)
(
6
x
3
+
5
x
2
−
100
x
+
125
)
(v)
(
2
x
3
−
5
x
2
−
50
x
+
125
)
Question
19
19.
Which of the following polynomials is not a multiple of
(
x
−
2
)
?
(i)
(
3
x
2
−
5
x
−
2
)
(ii)
(
x
2
−
6
x
+
8
)
(iii)
(
3
x
2
−
x
−
10
)
(iv)
(
x
2
−
3
x
+
2
)
(v)
(
3
x
2
+
2
x
−
5
)
Question
20
20.
Given
f
(
i
)
=
(
8
i
4
−
7
i
3
−
2
i
2
+
3
i
−
6
)
,
find
f
(
5
)
(i)
4082
(ii)
4085
(iii)
4084
(iv)
4083
(v)
4087
Question
21
21.
The remainder when
(
−
5
y
)
is divided by
9
is
(i)
(
−
1
)
(ii)
2
(iii)
(
−
3
)
(iv)
1
(v)
0
Question
22
22.
The degree of the polynomial
(
−
3
x
5
+
2
x
4
−
7
x
3
−
2
x
2
−
5
)
is
(i)
7
(ii)
4
(iii)
6
(iv)
5
(v)
3
Question
23
23.
Which of the following are true?
a)
A linear polynomial in one variable has only one root
b)
A polynomial of degree n has atmost n zeros
c)
Zero of a polynomial and root of the polynomial are synonymous
d)
If (x - a) is a factor of f(x), then f(a) = 0
e)
If (x + a) is a factor of f(x), then f(a) = 0
f)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
g)
Zero of a polynomial and zero polynomial are synonymous
(i)
{e,g,c}
(ii)
{g,b}
(iii)
{e,a}
(iv)
{e,d,f}
(v)
{a,b,c,d,f}
Question
24
24.
(
6
x
4
+
20
x
3
+
16
x
2
)
÷
(
3
x
2
+
4
x
)
(i)
(
x
2
+
4
x
)
(ii)
(
2
x
2
+
4
x
)
(iii)
(
2
x
2
−
4
x
)
(iv)
(
−
2
x
2
+
4
x
)
(v)
(
2
x
2
+
5
x
)
Question
25
25.
Which of the following polynomials is a multiple of
(
2
x
+
5
)
?
(i)
(
27
x
3
−
45
x
2
−
3
x
+
5
)
(ii)
(
9
x
3
+
9
x
2
−
x
−
1
)
(iii)
(
6
x
3
−
19
x
2
+
25
)
(iv)
(
6
x
3
−
11
x
2
−
12
x
+
5
)
(v)
(
12
x
3
−
20
x
2
−
75
x
+
125
)
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (ii)
5) (iv)
6) (i)
7) (i)
8) (v)
9) (iv)
10) (ii)
11) (iii)
12) (ii)
13) (iii)
14) (i)
15) (ii)
16) (v)
17) (iv)
18) (iii)
19) (v)
20) (iii)
21) (v)
22) (iv)
23) (v)
24) (ii)
25) (v)
