EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factor Theorem
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
(
4
x
4
+
4
x
3
−
12
x
2
−
4
x
+
8
)
÷
(
−
4
x
3
+
4
x
2
+
4
x
−
4
)
=
(i)
(
−
x
+
2
)
(ii)
(
x
−
2
)
(iii)
(
−
2
)
(iv)
(
−
2
x
−
2
)
(v)
(
−
x
−
2
)
Question
2
2.
Which of the following are true?
a)
If (x - a) is a factor of f(x), then f(a) = 0
b)
A polynomial of degree n has atmost n zeros
c)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
d)
If (x + a) is a factor of f(x), then f(a) = 0
e)
Zero of a polynomial and root of the polynomial are synonymous
f)
Zero of a polynomial and zero polynomial are synonymous
g)
A linear polynomial in one variable has only one root
(i)
{d,f,c}
(ii)
{d,e,g}
(iii)
{a,b,c,e,g}
(iv)
{f,b}
(v)
{d,a}
Question
3
3.
Find the value of
a
and
b
such that
b
x
4
+
a
x
3
−
52
x
2
+
2
x
+
12
is exactly divisible by
(
4
x
2
−
1
)
(i)
-8
,
17
(ii)
15
,
-9
(iii)
-8
,
16
(iv)
17
,
-7
(v)
-7
,
16
Question
4
4.
The value of the polynomial
(
4
z
4
+
7
z
3
−
2
z
2
−
3
z
+
9
)
at
z
=
4
is
(i)
1438
(ii)
1434
(iii)
1436
(iv)
1440
(v)
1437
Question
5
5.
Find the value of
k
such that
8
x
4
+
40
x
3
+
k
x
2
−
288
x
is exactly divisible by
(
x
+
6
)
(i)
-96
(ii)
-99
(iii)
-97
(iv)
-93
(v)
-95
Question
6
6.
Factorize
(
4
x
2
−
36
)
(i)
(
2
x
+
6
)
(
2
x
−
6
)
(ii)
(
2
x
+
6
)
(
3
x
−
6
)
(iii)
(
2
x
+
6
)
(
x
−
6
)
(iv)
(
2
x
+
6
)
(
−
6
)
(v)
(
2
x
+
6
)
(
5
x
−
6
)
Question
7
7.
Given
f
(
i
)
=
(
−
6
i
+
1
)
,
find
f
(
1
)
(i)
-6
(ii)
-4
(iii)
-5
(iv)
-3
(v)
-7
Question
8
8.
The quotient when
(
2
c
4
+
4
c
3
+
6
c
2
+
6
c
+
4
)
is divided by
(
c
−
3
)
is
(i)
(
−
c
3
+
10
c
2
+
36
c
+
114
)
(ii)
(
4
c
3
+
10
c
2
+
36
c
+
114
)
(iii)
(
2
c
3
+
10
c
2
+
36
c
+
114
)
(iv)
(
3
c
3
+
10
c
2
+
36
c
+
114
)
(v)
(
c
3
+
10
c
2
+
36
c
+
114
)
Question
9
9.
Given
f
(
x
)
=
(
x
2
−
6
x
−
6
)
,
find
f
(
(-5)
)
(i)
48
(ii)
51
(iii)
49
(iv)
50
(v)
47
Question
10
10.
Factorize
(
x
3
+
3
x
2
a
+
3
x
a
2
−
x
+
a
3
−
a
)
(i)
(
x
+
a
)
(
x
−
a
−
1
)
(
x
+
a
+
1
)
(ii)
(
x
+
a
)
(
x
+
a
−
1
)
(
x
−
a
+
1
)
(iii)
(
x
+
a
)
(
x
+
a
−
1
)
(
x
+
a
+
1
)
(iv)
(
x
−
a
)
(
x
−
a
−
1
)
(
x
+
a
+
1
)
(v)
(
x
−
a
)
(
x
+
a
−
1
)
(
x
−
a
+
1
)
Question
11
11.
(
24
x
5
−
44
x
4
+
40
x
2
−
24
x
+
4
)
divided by
(
−
6
x
3
+
11
x
2
−
6
x
+
1
)
=
(i)
(
−
4
x
2
+
x
+
4
)
(ii)
(
−
4
x
2
+
4
)
(iii)
(
−
4
x
2
−
x
+
4
)
(iv)
(
−
4
x
2
−
4
)
Question
12
12.
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)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
c)
If p(x) is divided by (x - a), the remainder is p(a)
d)
If p(a) = 0, then (x + a) perfectly divides p(x)
(i)
{b,a}
(ii)
{d,c}
(iii)
{b,c,a}
(iv)
{a,c}
(v)
{b,d,a}
Question
13
13.
The remainder when
(
−
a
−
2
)
is divided by
(
a
−
3
)
is
(i)
(
−
3
)
(ii)
(
−
4
)
(iii)
(
−
7
)
(iv)
(
−
6
)
(v)
(
−
5
)
Question
14
14.
(
16
x
4
+
4
x
3
)
÷
4
x
2
(i)
(
4
x
2
−
x
)
(ii)
(
3
x
2
+
x
)
(iii)
(
−
4
x
2
+
x
)
(iv)
(
4
x
2
+
2
x
)
(v)
(
4
x
2
+
x
)
Question
15
15.
The degree of the polynomial
(
−
6
w
2
+
9
w
−
7
)
is
(i)
2
(ii)
4
(iii)
3
(iv)
1
(v)
(-1)
Question
16
16.
The remainder when
(
6
q
2
−
7
q
)
is divided by
(
q
+
5
)
is
(i)
186
(ii)
188
(iii)
185
(iv)
183
(v)
184
Question
17
17.
Factorize
(
4
x
3
+
10
x
2
+
2
x
−
4
)
(i)
(
2
x
−
1
)
(
2
x
+
2
)
(
3
x
+
2
)
(ii)
(
2
x
−
1
)
(
x
+
2
)
(
2
x
+
2
)
(iii)
(
2
x
−
1
)
(
−
2
x
+
2
)
(
−
x
+
2
)
(iv)
(
2
x
−
1
)
2
(
x
+
2
)
(v)
(
2
x
−
1
)
(
3
x
+
2
)
(
4
x
+
2
)
Question
18
18.
The quotient when
(
−
2
i
3
+
i
+
5
)
is divided by
(
i
2
+
8
i
+
12
)
is
(i)
(
−
2
i
+
16
)
(ii)
16
(iii)
(
−
3
i
+
16
)
(iv)
(
−
5
i
+
16
)
(v)
(
−
i
+
16
)
Question
19
19.
If one of the roots of the cubic equation
(
270
x
3
−
717
x
2
+
613
x
−
168
)
=
0
is
8
9
,
find the remaining real roots
(i)
(
10
9
,
3
2
)
(ii)
(
8
7
,
5
4
)
(iii)
(
7
6
,
3
5
)
(iv)
(
2
3
,
5
6
)
(v)
(
8
11
,
9
8
)
Question
20
20.
If one of the roots of the cubic equation
(
x
3
−
36
x
)
=
0
is
0
,
find the remaining real roots
(i)
(
6
,
(
−
6
)
)
(ii)
(
(
−
1
)
,
5
)
(iii)
(
1
,
7
)
(iv)
(
3
,
8
)
(v)
(
(
−
3
)
,
4
)
Question
21
21.
Which of the following polynomials is a multiple of
(
x
−
2
)
?
(i)
(
9
x
3
+
39
x
2
+
52
x
+
20
)
(ii)
(
6
x
3
+
25
x
2
+
32
x
+
12
)
(iii)
(
9
x
3
−
9
x
2
−
28
x
+
20
)
(iv)
(
9
x
3
+
27
x
2
+
8
x
−
20
)
(v)
(
18
x
3
+
27
x
2
−
8
x
−
12
)
Question
22
22.
The remainder when
(
g
4
+
4
g
3
+
2
g
2
−
8
g
+
4
)
is divided by
(
g
2
−
3
g
−
28
)
is
(i)
(
340
g
+
1432
)
(ii)
(
343
g
+
1432
)
(iii)
(
339
g
+
1432
)
(iv)
(
342
g
+
1432
)
(v)
(
341
g
+
1432
)
Question
23
23.
The quotient when
(
−
6
d
2
)
is divided by
(
d
−
8
)
is
(i)
(
−
7
d
−
48
)
(ii)
(
−
8
d
−
48
)
(iii)
(
−
5
d
−
48
)
(iv)
(
−
4
d
−
48
)
(v)
(
−
6
d
−
48
)
Question
24
24.
The degree of the polynomial
(
−
7
u
5
−
8
u
3
+
8
u
2
−
8
u
−
7
)
is
(i)
7
(ii)
2
(iii)
6
(iv)
5
(v)
4
Question
25
25.
If
f
(
x
)
=
(
2
x
3
−
4
x
2
−
32
x
+
64
)
and
g
(
x
)
=
(
6
x
3
−
18
x
−
12
)
have a common factor, find the common factor
(i)
(
x
+
4
)
(ii)
(
2
x
−
4
)
(iii)
(
x
+
1
)
(iv)
(
3
x
+
3
)
(v)
(
x
−
4
)
Assignment Key
1) (v)
2) (iii)
3) (iii)
4) (v)
5) (i)
6) (i)
7) (iii)
8) (iii)
9) (iii)
10) (iii)
11) (ii)
12) (iv)
13) (v)
14) (v)
15) (i)
16) (iii)
17) (ii)
18) (i)
19) (iii)
20) (i)
21) (iii)
22) (v)
23) (v)
24) (iv)
25) (ii)
