EduSahara™ Assignment
Name : Factor Theorem
Chapter : Polynomials and Factorisation
Grade : SSC Grade IX
License : Non Commercial Use
Question
1
1.
Find the value of
k
such that
k
x
4
−
40
x
3
+
116
x
2
−
128
x
+
48
is exactly divisible by
(
2
x
−
2
)
(i)
2
(ii)
4
(iii)
7
(iv)
5
(v)
3
Question
2
2.
If
3
and
-2
are the zeros of the polynomial
f
(
x
)
=
a
x
4
−
6
x
3
−
22
x
2
+
b
x
, find the value of
a
and
b
(i)
11
,
3
(ii)
4
,
12
(iii)
4
,
13
(iv)
5
,
12
(v)
13
,
5
Question
3
3.
Find the value of
a
and
b
such that
8
x
4
+
b
x
3
+
a
x
2
+
84
x
+
90
is exactly divisible by
(
2
x
2
−
4
x
−
6
)
(i)
-25
,
-39
(ii)
-23
,
-37
(iii)
-38
,
-23
(iv)
-37
,
-24
(v)
-38
,
-24
Question
4
4.
If the polynomial
f
(
x
)
=
6
x
2
+
27
x
+
k
is exactly divisible by
(
2
x
+
5
)
,
find
k
(i)
31
(ii)
27
(iii)
30
(iv)
32
(v)
29
Question
5
5.
If the polynomials
a
x
2
+
3
x
+
12
and
5
x
2
+
a
x
−
8
leave the same remainder when divided by
(
x
−
2
)
,
find the value of
a
(i)
(-2)
(ii)
(-3)
(iii)
(-6)
(iv)
(-4)
(v)
(-1)
Question
6
6.
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)
b + d = 0
e)
d + e = 0
f)
a + b + c = d + e
(i)
{f,a,d}
(ii)
{e,c}
(iii)
{b,c,d}
(iv)
{a,b}
(v)
{e,b,c}
Question
7
7.
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 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)
If the degree of p(x) is less then the degree of d(x), we should not divide p(x) with d(x)
(i)
{a,c}
(ii)
{b,d}
(iii)
{a,d,c}
(iv)
{a,b,c}
(v)
{c,d}
Question
8
8.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
−
8
x
2
+
18
x
−
9
)
(i)
(
−
4
x
−
3
)
(
2
x
−
3
)
(ii)
(
−
4
x
+
6
)
(
2
x
+
3
)
(iii)
(
−
4
x
+
3
)
(
2
x
−
3
)
(iv)
(
−
4
x
+
3
)
(
2
x
+
3
)
(v)
(
−
4
x
−
3
)
(
2
x
+
3
)
Question
9
9.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
12
x
3
−
56
x
2
+
39
x
+
35
)
,
g
(
x
)
=
(
−
2
x
+
5
)
(ii)
f
(
x
)
=
(
−
12
x
3
+
92
x
2
−
225
x
+
175
)
,
g
(
x
)
=
(
3
x
+
4
)
(iii)
f
(
x
)
=
(
6
x
3
−
31
x
2
+
8
x
+
80
)
,
g
(
x
)
=
(
−
x
+
4
)
(iv)
f
(
x
)
=
(
18
x
3
−
69
x
2
−
19
x
+
140
)
,
g
(
x
)
=
(
2
x
+
1
)
(v)
f
(
x
)
=
(
6
x
3
−
37
x
2
+
24
x
+
112
)
,
g
(
x
)
=
(
−
3
x
+
5
)
Question
10
10.
Which of the following polynomials is a multiple of
(
2
x
+
1
)
?
(i)
(
3
x
3
+
8
x
2
+
3
x
−
2
)
(ii)
(
9
x
3
−
9
x
2
−
13
x
+
5
)
(iii)
(
18
x
3
−
9
x
2
−
29
x
−
10
)
(iv)
(
3
x
3
+
11
x
2
+
12
x
+
4
)
(v)
(
27
x
3
−
36
x
2
−
21
x
+
10
)
Question
11
11.
Which of the following polynomials has
(
3
x
−
2
)
as a factor ?
(i)
(
2
x
3
+
14
x
2
+
22
x
+
10
)
(ii)
(
3
x
3
+
4
x
2
−
45
x
+
50
)
(iii)
(
3
x
3
−
8
x
2
−
x
+
10
)
(iv)
(
2
x
3
−
6
x
−
4
)
(v)
(
9
x
3
+
24
x
2
−
95
x
+
50
)
Question
12
12.
If
f
(
x
)
=
(
2
x
3
+
21
x
2
+
67
x
+
60
)
and
g
(
x
)
=
(
9
x
3
+
39
x
2
−
48
)
have a common factor, find the common factor
(i)
(
3
x
+
4
)
(ii)
(
x
+
4
)
(iii)
(
x
+
5
)
(iv)
(
3
x
−
3
)
(v)
(
2
x
+
3
)
Question
13
13.
Which of the following polynomials is not a multiple of
(
x
+
1
)
?
(i)
(
2
x
2
+
3
x
+
1
)
(ii)
(
2
x
2
+
7
x
+
5
)
(iii)
(
x
2
+
4
x
+
3
)
(iv)
(
3
x
2
+
5
x
+
2
)
(v)
(
2
x
2
+
11
x
+
15
)
Assignment Key
1) (ii)
2) (ii)
3) (v)
4) (iii)
5) (ii)
6) (iii)
7) (v)
8) (iii)
9) (iii)
10) (iii)
11) (v)
12) (ii)
13) (v)
