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
+
36
x
3
+
84
x
2
−
4
x
−
120
is exactly divisible by
(
2
x
+
6
)
(i)
5
(ii)
6
(iii)
4
(iv)
3
(v)
2
Question
2
2.
If
4
and
-3
are the zeros of the polynomial
f
(
x
)
=
x
4
+
b
x
3
+
a
x
2
+
53
x
+
60
, find the value of
a
and
b
(i)
-13
,
-4
(ii)
-13
,
-5
(iii)
-4
,
-12
(iv)
-6
,
-14
(v)
-12
,
-5
Question
3
3.
Find the value of
a
and
b
such that
b
x
4
+
a
x
3
−
7
x
2
+
67
x
−
30
is exactly divisible by
(
2
x
2
−
x
−
10
)
(i)
5
,
-15
(ii)
-16
,
5
(iii)
3
,
-17
(iv)
-16
,
4
(v)
-15
,
4
Question
4
4.
If the polynomial
f
(
x
)
=
k
x
2
−
8
x
+
4
is exactly divisible by
(
3
x
−
2
)
,
find
k
(i)
3
(ii)
6
(iii)
2
(iv)
4
(v)
1
Question
5
5.
If the polynomials
a
x
2
+
2
x
−
14
and
−
6
x
2
+
a
x
+
36
leave the same remainder when divided by
(
x
+
2
)
,
find the value of
a
(i)
5
(ii)
3
(iii)
4
(iv)
7
(v)
6
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)
d + e = 0
b)
a + b + c + d + e = 0
c)
b + d = 0
d)
a + c + e = 0
e)
a + b + c = 0
f)
a + b + c = d + e
(i)
{e,c}
(ii)
{a,b}
(iii)
{e,b,c}
(iv)
{b,c,d}
(v)
{f,a,d}
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(x) is divided by (x - a), the remainder is p(a)
c)
If the degree of p(x) is less then the degree of d(x), we should not divide p(x) with d(x)
d)
If p(a) = 0, then (x + a) perfectly divides p(x)
(i)
{d,c}
(ii)
{a,c,b}
(iii)
{a,b}
(iv)
{b,c}
(v)
{a,d,b}
Question
8
8.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
−
4
x
2
−
4
x
+
8
)
(i)
(
2
x
+
4
)
(
−
2
x
+
2
)
(ii)
(
2
x
−
4
)
(
−
2
x
+
2
)
(iii)
(
2
x
−
4
)
(
−
2
x
−
2
)
(iv)
(
2
x
+
4
)
(
−
2
x
−
2
)
(v)
(
3
x
+
2
)
(
−
2
x
−
2
)
Question
9
9.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
−
6
x
3
−
55
x
2
−
86
x
+
35
)
,
g
(
x
)
=
(
−
3
x
+
8
)
(ii)
f
(
x
)
=
(
9
x
3
+
36
x
2
−
181
x
+
56
)
,
g
(
x
)
=
(
3
x
+
5
)
(iii)
f
(
x
)
=
(
12
x
3
−
8
x
2
−
79
x
+
40
)
,
g
(
x
)
=
(
−
2
x
+
1
)
(iv)
f
(
x
)
=
(
−
9
x
3
−
75
x
2
−
79
x
+
35
)
,
g
(
x
)
=
(
2
x
+
5
)
(v)
f
(
x
)
=
(
6
x
3
+
23
x
2
−
125
x
+
56
)
,
g
(
x
)
=
(
−
3
x
+
1
)
Question
10
10.
Which of the following polynomials is a multiple of
(
x
+
2
)
?
(i)
(
9
x
3
−
31
x
−
10
)
(ii)
(
9
x
3
+
18
x
2
−
16
x
−
32
)
(iii)
(
27
x
3
+
18
x
2
−
57
x
−
20
)
(iv)
(
27
x
3
+
9
x
2
−
48
x
−
16
)
(v)
(
9
x
3
+
9
x
2
−
34
x
−
40
)
Question
11
11.
Which of the following polynomials has
(
3
x
+
5
)
as a factor ?
(i)
(
9
x
3
+
21
x
2
−
33
x
−
45
)
(ii)
(
9
x
3
+
51
x
2
+
87
x
+
45
)
(iii)
(
3
x
3
−
14
x
2
+
3
x
+
20
)
(iv)
(
9
x
3
+
3
x
2
−
21
x
−
15
)
(v)
(
x
3
−
13
x
−
12
)
Question
12
12.
If
f
(
x
)
=
(
18
x
3
+
48
x
2
−
6
x
−
60
)
and
g
(
x
)
=
(
12
x
3
−
24
x
2
−
33
x
+
45
)
have a common factor, find the common factor
(i)
(
3
x
+
5
)
(ii)
(
2
x
−
5
)
(iii)
(
2
x
+
3
)
(iv)
(
2
x
+
4
)
(v)
(
3
x
−
3
)
Question
13
13.
Which of the following polynomials is not a multiple of
(
x
+
5
)
?
(i)
(
2
x
2
+
13
x
+
20
)
(ii)
(
x
2
+
4
x
−
5
)
(iii)
(
x
2
+
6
x
+
5
)
(iv)
(
2
x
2
+
15
x
+
25
)
(v)
(
x
2
+
9
x
+
20
)
Assignment Key
1) (iii)
2) (ii)
3) (iv)
4) (i)
5) (i)
6) (iv)
7) (iv)
8) (i)
9) (iii)
10) (ii)
11) (ii)
12) (v)
13) (i)
