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
8
x
3
+
12
x
2
+
k
x
−
24
is exactly divisible by
(
2
x
+
4
)
(i)
-17
(ii)
-19
(iii)
-21
(iv)
-20
(v)
-22
Question
2
2.
If
5
and
-3
are the zeros of the polynomial
f
(
x
)
=
2
x
4
+
x
3
−
37
x
2
+
b
x
+
a
, find the value of
a
and
b
(i)
-82
,
-46
(ii)
-45
,
-81
(iii)
-44
,
-81
(iv)
-80
,
-44
(v)
-45
,
-80
Question
3
3.
Find the value of
a
and
b
such that
a
x
4
+
12
x
3
−
12
x
2
+
b
x
−
24
is exactly divisible by
(
2
x
2
−
2
x
−
4
)
(i)
4
,
-43
(ii)
-45
,
3
(iii)
4
,
-44
(iv)
-43
,
5
(v)
5
,
-44
Question
4
4.
If the polynomial
f
(
x
)
=
6
x
2
+
k
x
−
30
is exactly divisible by
(
2
x
−
5
)
,
find
k
(i)
-2
(ii)
-1
(iii)
-3
(iv)
-5
(v)
-4
Question
5
5.
If the polynomials
a
x
2
+
5
x
+
37
and
−
3
x
2
+
a
x
+
3
leave the same remainder when divided by
(
x
+
2
)
,
find the value of
a
(i)
(-9)
(ii)
(-5)
(iii)
(-7)
(iv)
(-6)
(v)
(-3)
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)
a + b + c = 0
c)
d + e = 0
d)
a + b + c = d + e
e)
a + b + c + d + e = 0
f)
b + d = 0
(i)
{d,b,f}
(ii)
{c,a,e}
(iii)
{b,a}
(iv)
{c,e}
(v)
{a,e,f}
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)
{d,b}
(ii)
{a,b}
(iii)
{c,d,a}
(iv)
{c,a}
(v)
{c,b,a}
Question
8
8.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
12
x
2
−
22
x
+
10
)
(i)
(
−
2
x
+
2
)
(
−
6
x
+
5
)
(ii)
(
2
x
−
6
)
(
−
6
x
−
5
)
(iii)
(
−
2
x
−
2
)
(
−
6
x
−
5
)
(iv)
(
−
2
x
+
2
)
(
−
6
x
−
5
)
(v)
(
−
2
x
−
2
)
(
−
6
x
+
5
)
Question
9
9.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
3
x
3
+
47
x
2
+
214
x
+
240
)
,
g
(
x
)
=
(
−
3
x
+
7
)
(ii)
f
(
x
)
=
(
−
x
3
−
13
x
2
−
34
x
+
48
)
,
g
(
x
)
=
(
3
x
+
5
)
(iii)
f
(
x
)
=
(
−
3
x
3
−
35
x
2
−
46
x
+
336
)
,
g
(
x
)
=
(
−
x
+
1
)
(iv)
f
(
x
)
=
(
3
x
3
+
26
x
2
+
53
x
+
30
)
,
g
(
x
)
=
(
x
+
8
)
(v)
f
(
x
)
=
(
−
3
x
3
−
5
x
2
+
3
x
+
5
)
,
g
(
x
)
=
(
x
+
1
)
Question
10
10.
Which of the following polynomials is a multiple of
(
x
+
2
)
?
(i)
(
3
x
3
−
5
x
2
−
42
x
−
40
)
(ii)
(
2
x
3
−
5
x
2
−
22
x
−
15
)
(iii)
(
6
x
3
+
25
x
2
+
34
x
+
15
)
(iv)
(
9
x
3
+
36
x
2
+
47
x
+
20
)
(v)
(
6
x
3
−
13
x
2
−
73
x
−
60
)
Question
11
11.
Which of the following polynomials has
(
2
x
+
5
)
as a factor ?
(i)
(
2
x
3
+
8
x
2
−
14
x
−
20
)
(ii)
(
4
x
3
−
6
x
2
−
10
x
+
12
)
(iii)
(
8
x
3
+
12
x
2
−
8
x
−
12
)
(iv)
(
4
x
3
+
20
x
2
−
4
x
−
20
)
(v)
(
2
x
3
+
11
x
2
−
5
x
−
50
)
Question
12
12.
If
f
(
x
)
=
(
6
x
3
+
30
x
2
−
6
x
−
30
)
and
g
(
x
)
=
(
18
x
3
−
24
x
2
−
54
x
+
60
)
have a common factor, find the common factor
(i)
(
3
x
−
3
)
(ii)
(
x
+
5
)
(iii)
(
2
x
−
4
)
(iv)
(
2
x
+
2
)
(v)
(
3
x
+
5
)
Question
13
13.
Which of the following polynomials is not a multiple of
(
3
x
−
4
)
?
(i)
(
6
x
2
−
11
x
+
4
)
(ii)
(
2
x
2
−
5
x
+
2
)
(iii)
(
3
x
2
−
10
x
+
8
)
(iv)
(
9
x
2
−
6
x
−
8
)
(v)
(
3
x
2
−
7
x
+
4
)
Assignment Key
1) (iv)
2) (ii)
3) (iii)
4) (iii)
5) (iv)
6) (v)
7) (ii)
8) (i)
9) (v)
10) (i)
11) (v)
12) (i)
13) (ii)
