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
+
5
x
3
+
4
x
2
+
x
is exactly divisible by
(
x
+
1
)
(i)
-1
(ii)
2
(iii)
4
(iv)
3
(v)
1
Question
2
2.
If
4
and
(
-3
2
)
are the zeros of the polynomial
f
(
x
)
=
8
x
4
−
20
x
3
−
98
x
2
+
a
x
+
b
, find the value of
a
and
b
(i)
125
,
300
(ii)
299
,
124
(iii)
126
,
300
(iv)
125
,
301
(v)
301
,
126
Question
3
3.
Find the value of
a
and
b
such that
4
x
4
+
10
x
3
+
a
x
2
+
b
x
is exactly divisible by
(
2
x
2
+
9
x
−
5
)
(i)
-45
,
20
(ii)
19
,
-47
(iii)
-46
,
20
(iv)
-46
,
21
(v)
21
,
-45
Question
4
4.
If the polynomial
f
(
x
)
=
2
x
2
+
k
x
+
12
is exactly divisible by
(
x
−
3
)
,
find
k
(i)
-8
(ii)
-10
(iii)
-13
(iv)
-11
(v)
-9
Question
5
5.
If the polynomials
−
x
2
+
a
x
−
2
and
a
x
2
+
4
x
+
61
leave the same remainder when divided by
(
x
+
3
)
,
find the value of
a
(i)
(-4)
(ii)
(-8)
(iii)
(-5)
(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)
b + d = 0
b)
a + b + c + d + e = 0
c)
a + c + e = 0
d)
d + e = 0
e)
a + b + c = d + e
f)
a + b + c = 0
(i)
{d,a}
(ii)
{e,a,b}
(iii)
{e,b}
(iv)
{f,d,c}
(v)
{a,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 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(x) is divided by (x - a), the remainder is p(a)
(i)
{b,d}
(ii)
{c,d}
(iii)
{a,d,c}
(iv)
{a,c}
(v)
{a,b,c}
Question
8
8.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
−
18
x
2
+
30
x
−
12
)
(i)
(
−
6
x
−
6
)
(
3
x
+
2
)
(ii)
(
−
6
x
+
6
)
(
3
x
+
2
)
(iii)
(
−
2
x
+
5
)
(
3
x
+
2
)
(iv)
(
−
6
x
−
6
)
(
3
x
−
2
)
(v)
(
−
6
x
+
6
)
(
3
x
−
2
)
Question
9
9.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
−
4
x
3
+
4
x
2
+
133
x
+
245
)
,
g
(
x
)
=
(
−
x
+
5
)
(ii)
f
(
x
)
=
(
6
x
3
−
5
x
2
−
134
x
+
45
)
,
g
(
x
)
=
(
−
3
x
+
1
)
(iii)
f
(
x
)
=
(
−
4
x
3
−
4
x
2
+
161
x
+
441
)
,
g
(
x
)
=
(
2
x
+
5
)
(iv)
f
(
x
)
=
(
2
x
3
−
17
x
2
−
14
x
+
245
)
,
g
(
x
)
=
(
2
x
+
9
)
(v)
f
(
x
)
=
(
−
12
x
3
−
92
x
2
−
157
x
+
63
)
,
g
(
x
)
=
(
−
x
+
7
)
Question
10
10.
Which of the following polynomials is a multiple of
(
x
−
5
)
?
(i)
(
2
x
3
−
15
x
2
+
28
x
−
15
)
(ii)
(
6
x
3
−
23
x
2
+
29
x
−
12
)
(iii)
(
9
x
3
−
13
x
+
4
)
(iv)
(
27
x
3
−
9
x
2
−
48
x
+
16
)
(v)
(
18
x
3
−
27
x
2
−
32
x
+
48
)
Question
11
11.
Which of the following polynomials has
(
2
x
+
2
)
as a factor ?
(i)
(
3
x
3
−
3
x
2
−
3
x
+
3
)
(ii)
(
6
x
3
+
9
x
2
−
6
x
−
9
)
(iii)
(
6
x
3
−
9
x
2
−
15
x
+
18
)
(iv)
(
2
x
3
−
3
x
2
−
5
x
+
6
)
(v)
(
2
x
3
−
4
x
2
−
2
x
+
4
)
Question
12
12.
If
f
(
x
)
=
(
12
x
3
+
56
x
2
+
84
x
+
40
)
and
g
(
x
)
=
(
6
x
3
+
28
x
2
−
64
)
have a common factor, find the common factor
(i)
(
3
x
+
5
)
(ii)
(
x
+
4
)
(iii)
(
2
x
+
2
)
(iv)
(
2
x
+
4
)
(v)
(
3
x
−
4
)
Question
13
13.
Which of the following polynomials is not a multiple of
(
3
x
+
4
)
?
(i)
(
3
x
2
+
7
x
+
4
)
(ii)
(
6
x
2
+
5
x
−
25
)
(iii)
(
6
x
2
+
23
x
+
20
)
(iv)
(
3
x
2
−
2
x
−
8
)
(v)
(
9
x
2
−
3
x
−
20
)
Assignment Key
1) (ii)
2) (i)
3) (iii)
4) (ii)
5) (iii)
6) (v)
7) (ii)
8) (v)
9) (ii)
10) (i)
11) (v)
12) (iv)
13) (ii)
