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
4
x
4
+
2
x
3
+
k
x
2
+
72
is exactly divisible by
(
x
−
2
)
(i)
-38
(ii)
-35
(iii)
-39
(iv)
-37
(v)
-40
Question
2
2.
If
4
and
-3
are the zeros of the polynomial
f
(
x
)
=
a
x
4
−
3
x
3
−
25
x
2
+
b
x
+
180
, find the value of
a
and
b
(i)
2
,
39
(ii)
1
,
39
(iii)
40
,
2
(iv)
38
,
0
(v)
1
,
40
Question
3
3.
Find the value of
a
and
b
such that
8
x
4
−
36
x
3
+
36
x
2
+
a
x
+
b
is exactly divisible by
(
4
x
2
−
2
x
−
6
)
(i)
-49
,
31
(ii)
33
,
-48
(iii)
-47
,
33
(iv)
32
,
-47
(v)
32
,
-48
Question
4
4.
If the polynomial
f
(
x
)
=
6
x
2
+
k
x
−
15
is exactly divisible by
(
3
x
−
5
)
,
find
k
(i)
-2
(ii)
1
(iii)
0
(iv)
-4
(v)
-1
Question
5
5.
If the polynomials
−
3
x
2
+
a
x
+
18
and
a
x
2
+
6
x
−
12
leave the same remainder when divided by
(
x
+
2
)
,
find the value of
a
(i)
5
(ii)
3
(iii)
6
(iv)
4
(v)
7
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 + c + e = 0
c)
b + d = 0
d)
a + b + c + d + e = 0
e)
d + e = 0
f)
a + b + c = d + e
(i)
{f,a,d}
(ii)
{a,b}
(iii)
{e,b,c}
(iv)
{b,c,d}
(v)
{e,c}
Question
7
7.
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(x) is divided by (x - a), the remainder is p(a)
c)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
d)
If p(a) = 0, then (x + a) perfectly divides p(x)
(i)
{c,a}
(ii)
{c,d,a}
(iii)
{c,b,a}
(iv)
{a,b}
(v)
{d,b}
Question
8
8.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
−
18
x
2
+
3
x
+
1
)
(i)
(
6
x
−
1
)
(
−
3
x
+
1
)
(ii)
(
6
x
−
1
)
(
−
3
x
−
1
)
(iii)
(
6
x
+
1
)
(
−
3
x
−
1
)
(iv)
(
6
x
+
1
)
(
−
3
x
+
1
)
(v)
(
5
x
+
4
)
(
−
3
x
−
1
)
Question
9
9.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
6
x
3
+
59
x
2
+
158
x
+
120
)
,
g
(
x
)
=
(
2
x
+
5
)
(ii)
f
(
x
)
=
(
−
6
x
3
−
17
x
2
+
3
x
+
20
)
,
g
(
x
)
=
(
−
3
x
+
1
)
(iii)
f
(
x
)
=
(
9
x
3
−
13
x
+
4
)
,
g
(
x
)
=
(
x
+
5
)
(iv)
f
(
x
)
=
(
3
x
3
+
11
x
2
−
19
x
+
5
)
,
g
(
x
)
=
(
x
+
6
)
(v)
f
(
x
)
=
(
3
x
3
+
14
x
2
−
23
x
+
6
)
,
g
(
x
)
=
(
3
x
+
4
)
Question
10
10.
Which of the following polynomials is a multiple of
(
3
x
−
2
)
?
(i)
(
x
3
+
11
x
2
+
38
x
+
40
)
(ii)
(
3
x
3
+
13
x
2
−
11
x
−
5
)
(iii)
(
9
x
3
−
12
x
2
+
x
+
2
)
(iv)
(
3
x
3
+
28
x
2
+
69
x
+
20
)
(v)
(
x
3
+
5
x
2
+
2
x
−
8
)
Question
11
11.
Which of the following polynomials has
(
x
−
1
)
as a factor ?
(i)
(
2
x
3
+
3
x
2
−
11
x
−
6
)
(ii)
(
3
x
3
+
6
x
2
−
15
x
−
18
)
(iii)
(
18
x
3
+
39
x
2
+
27
x
+
6
)
(iv)
(
6
x
3
−
5
x
2
−
12
x
−
4
)
(v)
(
3
x
3
+
9
x
2
−
3
x
−
9
)
Question
12
12.
If
f
(
x
)
=
(
3
x
3
−
8
x
2
−
41
x
+
30
)
and
g
(
x
)
=
(
3
x
3
−
2
x
2
−
48
x
+
32
)
have a common factor, find the common factor
(i)
(
x
+
3
)
(ii)
(
x
+
4
)
(iii)
(
x
−
4
)
(iv)
(
3
x
−
2
)
(v)
(
x
−
5
)
Question
13
13.
Which of the following polynomials is not a multiple of
(
2
x
−
1
)
?
(i)
(
2
x
2
−
5
x
+
2
)
(ii)
(
2
x
2
+
x
−
1
)
(iii)
(
2
x
2
+
3
x
−
2
)
(iv)
(
x
2
+
3
x
+
2
)
(v)
(
2
x
2
−
3
x
+
1
)
Assignment Key
1) (i)
2) (ii)
3) (v)
4) (v)
5) (i)
6) (iv)
7) (iv)
8) (iv)
9) (i)
10) (iii)
11) (v)
12) (iv)
13) (iv)
