EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factor Theorem
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The remainder when
(
−
f
4
+
8
f
3
+
7
f
2
+
3
f
−
6
)
is divided by
(
f
2
−
5
f
−
14
)
is
(i)
(
86
f
+
106
)
(ii)
(
83
f
+
106
)
(iii)
(
87
f
+
106
)
(iv)
(
85
f
+
106
)
(v)
(
84
f
+
106
)
Question
2
2.
The value of the polynomial
(
−
3
n
2
−
9
n
−
6
)
at
n
=
5
is
(i)
-125
(ii)
-127
(iii)
-126
(iv)
-124
(v)
-129
Question
3
3.
The remainder when
(
−
6
b
)
is divided by
3
is
(i)
(
−
3
)
(ii)
0
(iii)
(
−
1
)
(iv)
2
(v)
1
Question
4
4.
The remainder when
(
4
p
2
+
9
p
−
2
)
is divided by
(
p
−
6
)
is
(i)
194
(ii)
196
(iii)
199
(iv)
197
(v)
195
Question
5
5.
(
2
x
3
+
6
x
2
)
÷
2
x
(i)
(
x
2
+
4
x
)
(ii)
3
x
(iii)
(
x
2
+
3
x
)
(iv)
(
x
2
−
3
x
)
(v)
(
−
x
2
+
3
x
)
Question
6
6.
If
f
(
x
)
=
(
9
x
3
−
31
x
−
10
)
and
g
(
x
)
=
(
18
x
3
+
66
x
2
+
68
x
+
16
)
have a common factor, find the common factor
(i)
(
x
−
2
)
(ii)
(
3
x
+
4
)
(iii)
(
2
x
+
4
)
(iv)
(
3
x
+
1
)
(v)
(
3
x
+
5
)
Question
7
7.
(
36
x
4
−
78
x
3
+
42
x
2
+
6
x
−
6
)
÷
(
−
18
x
3
+
21
x
2
−
3
)
=
(i)
(
−
2
x
+
2
)
(ii)
(
2
x
+
2
)
(iii)
(
−
2
x
−
2
)
(iv)
(
−
x
+
2
)
(v)
(
−
3
x
+
2
)
Question
8
8.
Which of the following polynomials has
(
2
x
+
2
)
as a factor ?
(i)
(
12
x
3
−
44
x
2
+
29
x
+
15
)
(ii)
(
12
x
3
−
2
x
2
−
20
x
−
6
)
(iii)
(
18
x
3
+
30
x
2
−
16
x
−
8
)
(iv)
(
8
x
3
−
16
x
2
−
34
x
+
60
)
(v)
(
12
x
3
−
14
x
2
−
56
x
+
40
)
Question
9
9.
The quotient when
(
5
m
2
−
9
m
)
is divided by
(
m
+
7
)
is
(i)
(
5
m
−
44
)
(ii)
(
8
m
−
44
)
(iii)
(
6
m
−
44
)
(iv)
(
3
m
−
44
)
(v)
(
4
m
−
44
)
Question
10
10.
The remainder when
(
−
2
e
2
)
is divided by
(
e
−
5
)
is
(i)
(
−
53
)
(ii)
(
−
50
)
(iii)
(
−
51
)
(iv)
(
−
47
)
(v)
(
−
49
)
Question
11
11.
Given
f
(
t
)
=
(
−
8
t
+
9
)
,
find
f
(
4
)
(i)
-26
(ii)
-20
(iii)
-22
(iv)
-24
(v)
-23
Question
12
12.
The quotient when
5
t
is divided by
(
−
6
)
is
(i)
(
−
5
6
t
)
(ii)
(
−
5
4
t
)
(iii)
(
−
7
6
t
)
(iv)
(
−
5
8
t
)
(v)
(
−
1
2
t
)
Question
13
13.
Given
f
(
k
)
=
(
2
k
4
+
8
k
3
+
9
k
2
−
8
k
−
9
)
,
find
f
(
5
)
(i)
2423
(ii)
2429
(iii)
2427
(iv)
2426
(v)
2425
Question
14
14.
If
(
x
−
a
)
is a factor of
x
3
−
a
x
2
+
8
x
+
24
,
find the value of
a
(i)
(-2)
(ii)
(-5)
(iii)
(-4)
(iv)
(-3)
(v)
(-1)
Question
15
15.
The value of the polynomial
(
7
n
3
+
4
n
2
−
6
n
)
at
n
=
(-2)
is
(i)
-25
(ii)
-28
(iii)
-31
(iv)
-27
(v)
-29
Question
16
16.
Which of the following are true?
a)
Degree of zero polynomial is zero
b)
Every polynomial is a binomial
c)
π
r
2
is a monomial
d)
A binomial has two and only two terms
e)
A binomial may have degree 3
(i)
{a,c,d}
(ii)
{a,c}
(iii)
{c,d,e}
(iv)
{b,d}
(v)
{a,b,e}
Question
17
17.
The remainder when
(
y
2
+
8
y
+
2
)
is divided by
(
y
+
3
)
is
(i)
(
−
11
)
(ii)
(
−
13
)
(iii)
(
−
16
)
(iv)
(
−
12
)
(v)
(
−
14
)
Question
18
18.
The quotient when
(
x
2
+
2
x
−
9
)
is divided by
(
x
+
9
)
is
(i)
(
4
x
−
7
)
(ii)
(
x
−
7
)
(iii)
(
−
2
x
−
7
)
(iv)
(
2
x
−
7
)
(v)
(
−
7
)
Question
19
19.
Which of the following polynomials is not a multiple of
(
2
x
−
5
)
?
(i)
(
2
x
2
−
7
x
+
5
)
(ii)
(
2
x
2
−
3
x
−
5
)
(iii)
(
x
2
−
1
)
(iv)
(
4
x
2
−
25
)
(v)
(
6
x
2
−
25
x
+
25
)
Question
20
20.
Factorize
(
36
x
2
+
50
x
y
+
16
y
2
)
(i)
(
9
x
+
8
y
)
(
4
x
−
2
y
)
(ii)
(
9
x
−
8
y
)
(
4
x
+
2
y
)
(iii)
(
9
x
+
8
y
)
(
4
x
+
2
y
)
(iv)
(
9
x
+
8
y
)
(
9
x
−
8
y
)
(v)
(
9
x
−
8
y
)
(
4
x
−
2
y
)
Question
21
21.
Factorize
(
2
x
3
−
12
x
2
−
26
x
+
84
)
(i)
(
x
−
2
)
(
−
x
−
7
)
6
(ii)
(
x
−
2
)
(
−
7
)
(
x
+
6
)
(iii)
(
x
−
2
)
(
x
−
7
)
(
2
x
+
6
)
(iv)
(
x
−
2
)
(
4
x
−
7
)
(
5
x
+
6
)
(v)
(
x
−
2
)
(
2
x
−
7
)
(
3
x
+
6
)
Question
22
22.
Which of the following are true?
a)
A polynomial of degree n has atmost n zeros
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)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
e)
If (x - a) is a factor of f(x), then f(a) = 0
f)
Zero of a polynomial and zero polynomial are synonymous
g)
A linear polynomial in one variable has only one root
(i)
{f,c}
(ii)
{a,c,d,e,g}
(iii)
{b,f,d}
(iv)
{b,e,g}
(v)
{b,a}
Question
23
23.
The quotient when
2
w
2
is divided by
(
w
−
8
)
is
(i)
16
(ii)
(
4
w
+
16
)
(iii)
(
3
w
+
16
)
(iv)
(
2
w
+
16
)
(v)
(
w
+
16
)
Question
24
24.
The quotient when
(
7
p
4
−
5
p
3
+
6
p
2
+
4
p
−
9
)
is divided by
(
p
2
+
4
p
−
45
)
is
(i)
(
10
p
2
−
33
p
+
453
)
(ii)
(
8
p
2
−
33
p
+
453
)
(iii)
(
5
p
2
−
33
p
+
453
)
(iv)
(
6
p
2
−
33
p
+
453
)
(v)
(
7
p
2
−
33
p
+
453
)
Question
25
25.
Factorize
(
x
2
+
2
x
a
−
2
x
+
a
2
−
2
a
−
48
)
(i)
(
x
−
a
+
6
)
(
x
+
a
+
8
)
(ii)
(
x
+
a
−
8
)
(
x
−
a
+
6
)
(iii)
(
x
+
a
+
6
)
(
x
+
a
−
8
)
(iv)
(
x
+
a
+
6
)
(
x
−
a
−
8
)
(v)
(
x
−
a
−
8
)
(
x
+
a
−
6
)
Assignment Key
1) (iv)
2) (iii)
3) (ii)
4) (ii)
5) (iii)
6) (iv)
7) (i)
8) (ii)
9) (i)
10) (ii)
11) (v)
12) (i)
13) (iv)
14) (iv)
15) (ii)
16) (iii)
17) (ii)
18) (ii)
19) (iii)
20) (iii)
21) (iii)
22) (ii)
23) (iv)
24) (v)
25) (iii)
