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
−
12
x
3
−
25
x
2
+
111
x
−
90
is exactly divisible by
(
2
x
−
5
)
(i)
6
(ii)
2
(iii)
3
(iv)
5
(v)
4
Question
2
2.
If
1
and
(
-1
2
)
are the zeros of the polynomial
f
(
x
)
=
8
x
4
−
4
x
3
+
b
x
2
+
4
x
+
a
, find the value of
a
and
b
(i)
4
,
-11
(ii)
5
,
-12
(iii)
-11
,
5
(iv)
-13
,
3
(v)
4
,
-12
Question
3
3.
Find the value of
a
and
b
such that
b
x
4
+
16
x
3
−
62
x
2
+
a
x
+
60
is exactly divisible by
(
4
x
2
−
2
x
−
20
)
(i)
-93
,
8
(ii)
7
,
-95
(iii)
-94
,
9
(iv)
9
,
-93
(v)
-94
,
8
Question
4
4.
If the polynomial
f
(
x
)
=
3
x
2
+
17
x
+
k
is exactly divisible by
(
x
+
6
)
,
find
k
(i)
-8
(ii)
-5
(iii)
-6
(iv)
-3
(v)
-7
Question
5
5.
If the polynomials
3
x
2
+
a
x
−
28
and
a
x
2
−
3
x
−
18
leave the same remainder when divided by
(
x
−
2
)
,
find the value of
a
(i)
3
(ii)
7
(iii)
2
(iv)
4
(v)
5
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 + c + e = 0
b)
b + d = 0
c)
a + b + c = d + e
d)
a + b + c = 0
e)
a + b + c + d + e = 0
f)
d + e = 0
(i)
{d,a,b}
(ii)
{c,a}
(iii)
{a,b,e}
(iv)
{f,c,e}
(v)
{d,b}
Question
7
7.
Which of the following are true ?
a)
If p(a) = 0, then (x + a) perfectly divides p(x)
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(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)
{d,c}
(ii)
{b,c}
(iii)
{a,b}
(iv)
{a,d,b}
(v)
{a,c,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
−
24
x
−
20
)
(i)
(
−
x
+
5
)
(
4
x
+
4
)
(ii)
(
−
x
−
5
)
(
4
x
+
4
)
(iii)
(
3
x
+
2
)
(
4
x
−
4
)
(iv)
(
−
x
+
5
)
(
4
x
−
4
)
(v)
(
−
x
−
5
)
(
4
x
−
4
)
Question
9
9.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
2
x
3
+
15
x
2
+
37
x
+
30
)
,
g
(
x
)
=
(
−
2
x
+
1
)
(ii)
f
(
x
)
=
(
x
3
+
14
x
2
+
51
x
+
54
)
,
g
(
x
)
=
(
2
x
+
5
)
(iii)
f
(
x
)
=
(
−
12
x
3
−
40
x
2
−
17
x
+
20
)
,
g
(
x
)
=
(
3
x
+
4
)
(iv)
f
(
x
)
=
(
−
6
x
3
−
17
x
2
−
6
x
+
8
)
,
g
(
x
)
=
(
x
+
3
)
(v)
f
(
x
)
=
(
−
2
x
3
−
9
x
2
−
7
x
+
6
)
,
g
(
x
)
=
(
x
+
9
)
Question
10
10.
Which of the following polynomials is a multiple of
(
3
x
+
1
)
?
(i)
(
4
x
3
+
8
x
2
+
x
−
3
)
(ii)
(
12
x
3
−
4
x
2
−
25
x
+
12
)
(iii)
(
6
x
3
+
5
x
2
−
2
x
−
1
)
(iv)
(
3
x
3
+
14
x
2
−
9
x
−
20
)
(v)
(
6
x
3
+
31
x
2
−
7
x
−
60
)
Question
11
11.
Which of the following polynomials has
(
3
x
−
5
)
as a factor ?
(i)
(
4
x
3
−
6
x
2
−
18
x
+
20
)
(ii)
(
18
x
3
+
78
x
2
+
104
x
+
40
)
(iii)
(
6
x
3
−
17
x
2
+
x
+
10
)
(iv)
(
6
x
3
+
16
x
2
−
2
x
−
20
)
(v)
(
18
x
3
−
63
x
2
+
25
x
+
50
)
Question
12
12.
If
f
(
x
)
=
(
12
x
3
−
14
x
2
−
28
x
+
30
)
and
g
(
x
)
=
(
18
x
3
+
9
x
2
−
23
x
+
6
)
have a common factor, find the common factor
(i)
(
2
x
−
2
)
(ii)
(
3
x
−
1
)
(iii)
(
2
x
+
3
)
(iv)
(
3
x
−
5
)
(v)
(
3
x
−
2
)
Question
13
13.
Which of the following polynomials is not a multiple of
(
x
+
2
)
?
(i)
(
2
x
2
+
5
x
+
2
)
(ii)
(
x
2
−
4
)
(iii)
(
2
x
2
+
x
−
6
)
(iv)
(
3
x
2
−
5
x
−
2
)
(v)
(
3
x
2
+
7
x
+
2
)
Assignment Key
1) (v)
2) (v)
3) (v)
4) (iii)
5) (iv)
6) (iii)
7) (ii)
8) (ii)
9) (iii)
10) (iii)
11) (v)
12) (iii)
13) (iv)
