EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factorisation
Grade : SSC Grade VIII
License : Non Commercial Use
Question
1
1.
Which of the following is not an irreducible factor of
(
x
2
y
+
x
y
2
+
x
y
)
?
(i)
y
(ii)
x
(iii)
x
y
(iv)
(
x
+
y
+
1
)
Question
2
2.
(
8
x
4
+
10
x
3
)
÷
2
x
2
(i)
(
3
x
2
+
5
x
)
(ii)
(
4
x
2
+
5
x
)
(iii)
(
4
x
2
+
6
x
)
(iv)
(
4
x
2
−
5
x
)
(v)
(
−
4
x
2
+
5
x
)
Question
3
3.
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
4
4.
If
(
−
3
a
+
3
b
)
✕
A =
(
−
27
a
3
+
81
a
2
b
−
81
a
b
2
+
27
b
3
)
,
then A =
(i)
(
9
a
2
−
20
a
b
+
9
b
2
)
(ii)
(
8
a
2
−
18
a
b
+
9
b
2
)
(iii)
(
9
a
2
−
15
a
b
+
9
b
2
)
(iv)
(
9
a
2
−
18
a
b
+
9
b
2
)
(v)
(
10
a
2
−
18
a
b
+
9
b
2
)
Question
5
5.
Which of the following is a factor of
45
x
4
y
4
z
?
(i)
9
y
5
z
(ii)
9
x
4
y
z
2
(iii)
9
y
z
(iv)
9
y
z
2
(v)
x
5
y
z
Question
6
6.
Factorize
(
32
a
2
b
+
72
a
b
2
)
(i)
8
a
b
(
−
4
a
−
9
b
)
(ii)
8
a
(
4
a
+
9
b
)
(iii)
8
a
b
(
4
a
−
9
b
)
(iv)
8
a
b
(
4
a
+
9
b
)
(v)
8
b
(
4
a
−
9
b
)
Question
7
7.
Find the prime factorization of
35
(i)
5
✕
7
(ii)
4
✕
7
(iii)
5
✕
5
(iv)
5
✕
7
2
(v)
5
✕
9
Question
8
8.
The quotient of
(
−
8
a
3
+
120
a
b
c
−
64
b
3
−
125
c
3
)
÷
(
−
2
a
−
4
b
−
5
c
)
is
(i)
(
4
a
2
−
11
a
b
−
10
a
c
+
16
b
2
−
20
b
c
+
25
c
2
)
(ii)
(
4
a
2
−
5
a
b
−
10
a
c
+
16
b
2
−
20
b
c
+
25
c
2
)
(iii)
(
4
a
2
−
8
a
b
−
10
a
c
+
16
b
2
−
20
b
c
+
25
c
2
)
(iv)
(
3
a
2
−
8
a
b
−
10
a
c
+
16
b
2
−
20
b
c
+
25
c
2
)
(v)
(
5
a
2
−
8
a
b
−
10
a
c
+
16
b
2
−
20
b
c
+
25
c
2
)
Question
9
9.
(
4
x
4
+
48
x
3
+
144
x
2
+
128
x
)
÷
(
2
x
2
+
20
x
+
32
)
(i)
(
−
2
x
2
+
4
x
)
(ii)
(
2
x
2
+
4
x
)
(iii)
(
2
x
2
+
3
x
)
(iv)
(
2
x
2
+
5
x
)
(v)
(
2
x
2
−
4
x
)
Question
10
10.
Factorize
(
f
4
−
256
)
(i)
(
f
2
+
16
)
(
f
2
−
8
)
(ii)
(
f
+
4
)
(
f
+
4
)
(
f
−
4
)
(iii)
(
f
+
4
)
(
f
−
4
)
(
f
2
−
8
)
(iv)
(
f
+
4
)
(
f
−
4
)
(
f
2
+
16
)
(v)
(
f
+
4
)
(
f
−
4
)
(
f
−
4
)
Question
11
11.
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)
If p(x) is divided by (x - a), the remainder is p(a)
d)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
(i)
{a,c}
(ii)
{b,a}
(iii)
{b,c,a}
(iv)
{d,c}
(v)
{b,d,a}
Question
12
12.
Factorize
(
a
−
b
)
3
+
(
b
−
c
)
3
+
(
c
−
a
)
3
(i)
3
(
a
−
b
)
(
b
+
c
)
(
c
−
a
)
(ii)
3
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
(iii)
3
(
a
−
b
)
(
b
−
c
)
(
c
+
a
)
(iv)
3
(
a
−
b
)
(
b
+
c
)
(
c
+
a
)
(v)
3
(
a
+
b
)
(
b
−
c
)
(
c
−
a
)
Question
13
13.
The quotient of
(
4
a
2
−
8
a
b
+
4
b
2
)
÷
(
2
a
−
2
b
)
is
(i)
(
2
a
−
2
b
)
(ii)
(
3
a
−
2
b
)
(iii)
(
a
−
2
b
)
(iv)
(
2
a
−
5
b
)
(v)
(
2
a
+
b
)
Question
14
14.
The quotient of
(
125
a
3
−
150
a
2
b
+
60
a
b
2
−
8
b
3
)
÷
(
5
a
−
2
b
)
is
(i)
(
25
a
2
−
23
a
b
+
4
b
2
)
(ii)
(
25
a
2
−
20
a
b
+
4
b
2
)
(iii)
(
24
a
2
−
20
a
b
+
4
b
2
)
(iv)
(
25
a
2
−
17
a
b
+
4
b
2
)
(v)
(
26
a
2
−
20
a
b
+
4
b
2
)
Question
15
15.
The quotient when
(
8
q
5
−
8
q
4
−
6
q
3
+
9
q
2
+
6
q
+
5
)
is divided by
(
q
−
4
)
is
(i)
(
10
q
4
+
24
q
3
+
90
q
2
+
369
q
+
1482
)
(ii)
(
8
q
4
+
24
q
3
+
90
q
2
+
369
q
+
1482
)
(iii)
(
7
q
4
+
24
q
3
+
90
q
2
+
369
q
+
1482
)
(iv)
(
9
q
4
+
24
q
3
+
90
q
2
+
369
q
+
1482
)
(v)
(
5
q
4
+
24
q
3
+
90
q
2
+
369
q
+
1482
)
Question
16
16.
The quotient of
(
−
a
3
+
8
b
3
)
÷
(
−
a
+
2
b
)
is
(i)
(
a
2
+
4
b
2
)
(ii)
(
a
2
+
4
a
b
+
4
b
2
)
(iii)
(
2
a
2
+
2
a
b
+
4
b
2
)
(iv)
(
2
a
b
+
4
b
2
)
(v)
(
a
2
+
2
a
b
+
4
b
2
)
Question
17
17.
(
−
2
x
3
+
x
2
+
7
x
−
6
)
÷
(
x
2
+
x
−
2
)
=
(i)
(
−
2
x
+
3
)
(ii)
(
−
x
+
3
)
(iii)
(
−
2
x
−
3
)
(iv)
(
−
3
x
+
3
)
(v)
(
2
x
+
3
)
Question
18
18.
Factorize
(
48
x
2
+
44
x
y
−
14
y
2
)
(i)
(
6
x
+
7
y
)
(
8
x
+
2
y
)
(ii)
(
6
x
−
7
y
)
(
8
x
+
2
y
)
(iii)
(
6
x
+
7
y
)
(
6
x
−
7
y
)
(iv)
(
6
x
+
7
y
)
(
8
x
−
2
y
)
(v)
(
6
x
−
7
y
)
(
8
x
−
2
y
)
Question
19
19.
Factorize
(
25
a
2
+
10
a
b
+
20
a
c
+
b
2
+
4
b
c
+
4
c
2
)
(i)
(
−
4
a
−
b
−
2
c
)
(
−
4
a
−
b
−
2
c
)
(ii)
(
−
6
a
−
b
−
2
c
)
(
−
6
a
−
b
−
2
c
)
(iii)
(
−
5
a
−
3
b
−
2
c
)
(
−
5
a
−
3
b
−
2
c
)
(iv)
(
−
5
a
+
2
b
−
2
c
)
(
−
5
a
+
b
−
2
c
)
(v)
(
−
5
a
−
b
−
2
c
)
(
−
5
a
−
b
−
2
c
)
Question
20
20.
The quotient when
(
9
d
2
−
9
d
+
8
)
is divided by
(
d
+
8
)
is
(i)
(
12
d
−
81
)
(ii)
(
10
d
−
81
)
(iii)
(
8
d
−
81
)
(iv)
(
9
d
−
81
)
(v)
(
6
d
−
81
)
Question
21
21.
(
18
x
5
−
105
x
4
+
174
x
3
−
39
x
2
−
84
x
+
36
)
divided by
(
3
x
3
−
18
x
2
+
33
x
−
18
)
=
(i)
(
6
x
2
−
2
)
(ii)
(
6
x
2
−
x
−
2
)
(iii)
(
6
x
2
+
x
−
2
)
(iv)
(
6
x
2
+
2
x
−
2
)
(v)
(
6
x
2
+
x
+
2
)
Question
22
22.
Which of the following is a factor of
(
7
x
5
+
y
3
z
)
?
(i)
7
y
2
(ii)
y
3
z
(iii)
7
x
5
(iv)
no factors
(v)
7
x
z
Question
23
23.
If
(
5
a
−
b
)
✕
A =
(
125
a
3
−
75
a
2
b
+
15
a
b
2
−
b
3
)
,
then A =
(i)
(
25
a
2
−
7
a
b
+
b
2
)
(ii)
(
25
a
2
−
12
a
b
+
b
2
)
(iii)
(
26
a
2
−
10
a
b
+
b
2
)
(iv)
(
25
a
2
−
10
a
b
+
b
2
)
(v)
(
24
a
2
−
10
a
b
+
b
2
)
Question
24
24.
Factorize
(
21
x
y
+
15
y
2
)
(i)
3
y
(
7
x
+
5
y
)
(ii)
3
y
(
−
7
x
−
5
y
)
(iii)
3
x
(
7
x
+
5
y
)
(iv)
3
y
(
7
x
−
5
y
)
(v)
3
x
(
7
x
−
5
y
)
Question
25
25.
Factorize
(
a
2
+
2
a
b
+
b
2
)
(i)
(
a
+
4
b
)
(
a
+
3
b
)
(ii)
(
a
−
b
)
(
a
−
2
b
)
(iii)
(
2
a
+
b
)
(
2
a
+
b
)
(iv)
b
b
(v)
(
a
+
b
)
(
a
+
b
)
Assignment Key
1) (iii)
2) (ii)
3) (iii)
4) (iv)
5) (iii)
6) (iv)
7) (i)
8) (iii)
9) (ii)
10) (iv)
11) (i)
12) (ii)
13) (i)
14) (ii)
15) (ii)
16) (v)
17) (i)
18) (iv)
19) (v)
20) (iv)
21) (iii)
22) (iv)
23) (iv)
24) (i)
25) (v)
