EduSahara™ Assignment
Name : Factor Theorem
Chapter : Polynomials
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
Find the value of
k
such that
2
x
3
+
5
x
2
+
k
x
is exactly divisible by
(
x
+
5
)
(i)
-25
(ii)
-26
(iii)
-24
(iv)
-27
(v)
-23
Question
2
2.
If
2
and
-5
are the zeros of the polynomial
f
(
x
)
=
a
x
4
−
46
x
2
+
b
x
+
80
, find the value of
a
and
b
(i)
35
,
1
(ii)
37
,
3
(iii)
3
,
36
(iv)
2
,
37
(v)
2
,
36
Question
3
3.
Find the value of
a
and
b
such that
a
x
4
+
16
x
3
+
b
x
2
−
64
x
+
96
is exactly divisible by
(
4
x
2
−
16
)
(i)
8
,
-55
(ii)
9
,
-56
(iii)
-57
,
7
(iv)
-55
,
9
(v)
8
,
-56
Question
4
4.
If the polynomial
f
(
x
)
=
k
x
2
+
5
x
−
6
is exactly divisible by
(
x
+
6
)
,
find
k
(i)
1
(ii)
2
(iii)
3
(iv)
-1
(v)
0
Question
5
5.
If the polynomials
a
x
2
−
2
x
−
36
and
−
4
x
2
+
a
x
+
24
leave the same remainder when divided by
(
x
−
3
)
,
find the value of
a
(i)
5
(ii)
4
(iii)
3
(iv)
8
(v)
6
Question
6
6.
Which of the following are true?
a)
If (x + a) is a factor of f(x), then f(a) = 0
b)
If (x - a) is a factor of f(x), then f(a) = 0
c)
Zero of a polynomial and root of the polynomial are synonymous
d)
A polynomial of degree n has atmost n zeros
e)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
f)
Zero of a polynomial and zero polynomial are synonymous
g)
A linear polynomial in one variable has only one root
(i)
{a,e,g}
(ii)
{f,c}
(iii)
{b,c,d,e,g}
(iv)
{a,f,d}
(v)
{a,b}
Question
7
7.
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)
d + e = 0
c)
b + d = 0
d)
a + c + e = 0
e)
a + b + c = d + e
f)
a + b + c + d + e = 0
(i)
{e,a,f}
(ii)
{b,d}
(iii)
{a,c}
(iv)
{c,d,f}
(v)
{b,c,d}
Question
8
8.
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(a) = 0, then (x + a) perfectly divides p(x)
c)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
d)
If p(x) is divided by (x - a), the remainder is p(a)
(i)
{a,d}
(ii)
{b,d,a}
(iii)
{b,c,a}
(iv)
{b,a}
(v)
{c,d}
Question
9
9.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
15
x
2
−
5
x
−
20
)
(i)
(
−
3
x
+
3
)
(
5
x
−
5
)
(ii)
(
3
x
−
4
)
(
5
x
−
5
)
(iii)
(
3
x
+
4
)
(
5
x
−
5
)
(iv)
(
3
x
−
4
)
(
5
x
+
5
)
(v)
(
3
x
+
4
)
(
5
x
+
5
)
Question
10
10.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
−
6
x
3
−
23
x
2
+
6
x
+
63
)
,
g
(
x
)
=
(
x
+
3
)
(ii)
f
(
x
)
=
(
−
6
x
3
−
29
x
2
+
154
x
+
441
)
,
g
(
x
)
=
(
−
x
+
1
)
(iii)
f
(
x
)
=
(
−
6
x
3
−
5
x
2
+
102
x
+
189
)
,
g
(
x
)
=
(
x
+
7
)
(iv)
f
(
x
)
=
(
2
x
3
+
3
x
2
−
68
x
+
63
)
,
g
(
x
)
=
(
−
2
x
+
3
)
(v)
f
(
x
)
=
(
4
x
3
+
4
x
2
−
141
x
+
189
)
,
g
(
x
)
=
(
3
x
+
7
)
Question
11
11.
Which of the following polynomials is a multiple of
(
x
−
2
)
?
(i)
(
3
x
3
−
4
x
2
−
48
x
+
64
)
(ii)
(
3
x
3
+
2
x
2
−
32
x
+
32
)
(iii)
(
9
x
3
−
6
x
2
−
11
x
+
4
)
(iv)
(
x
3
+
x
2
−
16
x
−
16
)
(v)
(
3
x
3
−
10
x
2
−
9
x
+
4
)
Question
12
12.
Which of the following polynomials has
(
3
x
+
1
)
as a factor ?
(i)
(
6
x
3
+
5
x
2
−
44
x
−
15
)
(ii)
(
6
x
3
+
4
x
2
−
34
x
+
24
)
(iii)
(
12
x
3
−
34
x
2
+
30
x
−
8
)
(iv)
(
4
x
3
−
2
x
2
−
32
x
+
30
)
(v)
(
12
x
3
−
52
x
2
+
63
x
−
20
)
Question
13
13.
If
f
(
x
)
=
(
2
x
3
+
3
x
2
−
5
x
−
6
)
and
g
(
x
)
=
(
6
x
3
+
20
x
2
+
8
x
−
16
)
have a common factor, find the common factor
(i)
(
2
x
−
3
)
(ii)
(
3
x
−
2
)
(iii)
(
x
+
1
)
(iv)
(
2
x
+
4
)
(v)
(
x
+
2
)
Question
14
14.
Which of the following polynomials is not a multiple of
(
x
+
4
)
?
(i)
(
2
x
2
+
9
x
+
4
)
(ii)
(
x
2
+
6
x
+
8
)
(iii)
(
x
2
+
5
x
+
4
)
(iv)
(
x
2
+
3
x
+
2
)
(v)
(
x
2
+
3
x
−
4
)
Assignment Key
1) (i)
2) (v)
3) (v)
4) (i)
5) (i)
6) (iii)
7) (iv)
8) (i)
9) (iv)
10) (i)
11) (ii)
12) (i)
13) (v)
14) (iv)
