EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factorisation
Grade : CBSE Grade VIII
License : Non Commercial Use
Question
1
1.
Factorize
a
2
c
2
−
b
2
c
2
−
a
2
d
2
+
b
2
d
2
(i)
(
a
+
b
)
(
a
−
b
)
(
c
+
d
)
(
c
−
d
)
(ii)
(
a
+
b
)
(
a
−
b
)
(
b
+
d
)
(
c
−
d
)
(iii)
(
a
+
c
)
(
a
−
c
)
(
b
+
d
)
(
b
−
d
)
(iv)
(
a
+
b
)
(
a
−
b
)
(
c
+
d
)
(
b
−
d
)
(v)
(
a
+
b
)
(
a
−
c
)
(
c
+
d
)
(
c
−
d
)
Question
2
2.
The quotient when
(
−
f
4
−
9
f
3
+
9
f
2
+
f
−
9
)
is divided by
(
f
2
−
2
f
−
24
)
is
(i)
(
−
11
f
−
37
)
(ii)
(
−
f
2
−
11
f
−
37
)
(iii)
(
f
2
−
11
f
−
37
)
(iv)
(
−
3
f
2
−
11
f
−
37
)
(v)
(
−
2
f
2
−
11
f
−
37
)
Question
3
3.
c
4
=
(i)
4
✕
c
✕
c
✕
c
✕
c
(ii)
c
✕
c
✕
c
(iii)
−
c
✕
c
✕
c
✕
c
(iv)
c
✕
c
✕
c
✕
c
✕
c
(v)
c
✕
c
✕
c
✕
c
Question
4
4.
(
2
x
4
+
8
x
3
)
÷
2
x
2
(i)
4
x
(ii)
(
x
2
+
5
x
)
(iii)
(
x
2
−
4
x
)
(iv)
(
x
2
+
4
x
)
(v)
(
−
x
2
+
4
x
)
Question
5
5.
The quotient when
(
−
7
k
2
+
6
k
+
7
)
is divided by
(
k
+
7
)
is
(i)
(
−
10
k
+
55
)
(ii)
(
−
6
k
+
55
)
(iii)
(
−
7
k
+
55
)
(iv)
(
−
4
k
+
55
)
(v)
(
−
8
k
+
55
)
Question
6
6.
Factorize
(
21
x
y
+
15
y
2
)
(i)
3
x
(
7
x
−
5
y
)
(ii)
3
y
(
−
7
x
−
5
y
)
(iii)
3
y
(
7
x
−
5
y
)
(iv)
3
y
(
7
x
+
5
y
)
(v)
3
x
(
7
x
+
5
y
)
Question
7
7.
Factorize
(
x
2
+
11
x
+
28
)
(i)
(
x
−
7
)
(
x
−
4
)
(ii)
(
x
+
7
)
(
x
+
4
)
(iii)
(
x
−
7
)
(
x
+
4
)
(iv)
(
x
+
7
)
(
x
−
4
)
Question
8
8.
Factorize
49
a
3
−
36
a
(i)
(
7
a
−
6
)
(
7
a
2
+
6
)
a
(ii)
(
7
a
2
+
6
)
(
6
a
−
7
)
a
(iii)
(
7
a
+
6
)
(
7
a
−
6
)
a
(iv)
(
7
a
+
6
)
(
7
a
2
+
6
)
a
(v)
(
7
a
+
6
)
(
6
a
−
7
)
a
Question
9
9.
The remainder when
(
2
a
−
2
)
is divided by
(
a
−
3
)
is
(i)
2
(ii)
5
(iii)
7
(iv)
4
(v)
3
Question
10
10.
Which of the following are true?
a)
A binomial may have degree 3
b)
π
r
2
is a monomial
c)
Degree of zero polynomial is zero
d)
A binomial has two and only two terms
e)
Every polynomial is a binomial
(i)
{c,a}
(ii)
{c,a,b}
(iii)
{a,b,d}
(iv)
{c,e,d}
(v)
{e,b}
Question
11
11.
Factorize
(
18
x
2
−
27
x
y
−
81
y
2
)
(i)
(
6
x
+
9
y
)
(
6
x
−
9
y
)
(ii)
(
6
x
+
9
y
)
(
3
x
+
9
y
)
(iii)
(
6
x
−
9
y
)
(
3
x
−
9
y
)
(iv)
(
6
x
+
9
y
)
(
3
x
−
9
y
)
(v)
(
6
x
−
9
y
)
(
3
x
+
9
y
)
Question
12
12.
The remainder when
(
5
k
2
−
2
k
−
3
)
is divided by
(
k
−
6
)
is
(i)
162
(ii)
165
(iii)
168
(iv)
164
(v)
166
Question
13
13.
(
24
x
4
+
124
x
3
+
196
x
2
+
96
x
)
÷
(
6
x
2
+
25
x
+
24
)
(i)
(
4
x
2
+
3
x
)
(ii)
(
4
x
2
−
4
x
)
(iii)
(
−
4
x
2
+
4
x
)
(iv)
(
4
x
2
+
5
x
)
(v)
(
4
x
2
+
4
x
)
Question
14
14.
Factorize
(
x
4
+
x
2
−
6
)
(i)
(
x
2
+
3
)
(
x
2
+
2
)
(ii)
(
x
2
−
3
)
(
x
2
+
2
)
(iii)
(
x
2
−
3
)
(
x
2
−
2
)
(iv)
(
x
2
−
2
)
(
x
2
+
2
)
(v)
(
x
2
+
3
)
(
x
2
−
2
)
Question
15
15.
Factorize
(
16
a
2
−
8
a
b
+
b
2
)
(i)
(
3
a
−
b
)
(
3
a
−
b
)
(ii)
(
4
a
−
4
b
)
(
4
a
−
3
b
)
(iii)
(
5
a
−
b
)
(
5
a
−
b
)
(iv)
(
4
a
+
b
)
(
4
a
+
b
)
(v)
(
4
a
−
b
)
(
4
a
−
b
)
Question
16
16.
Factorize
(
x
4
+
6
x
3
−
52
x
2
−
216
x
+
576
)
(i)
(
x
−
6
)
(
2
x
−
2
)
(
2
x
+
6
)
(
2
x
+
8
)
(ii)
(
x
−
6
)
(
3
x
−
2
)
(
4
x
+
6
)
(
4
x
+
8
)
(iii)
(
x
−
6
)
(
−
2
)
6
8
(iv)
(
x
−
6
)
(
−
x
−
2
)
(
−
x
+
6
)
(
−
2
x
+
8
)
(v)
(
x
−
6
)
(
x
−
2
)
(
x
+
6
)
(
x
+
8
)
Question
17
17.
Factorize
(
a
x
+
b
y
)
2
−
(
a
x
−
b
y
)
2
(i)
2
(
a
x
)
2
(
b
y
)
2
(ii)
4
(
a
x
)
2
(
b
y
)
2
(iii)
2
a
x
b
y
(iv)
4
a
x
b
y
Question
18
18.
The remainder when
8
c
is divided by
1
is
(i)
(
−
1
)
(ii)
2
(iii)
1
(iv)
(
−
2
)
(v)
0
Question
19
19.
k
3
l
3
m
2
=
(i)
k
✕
k
✕
k
✕
l
✕
l
✕
l
✕
m
✕
m
(ii)
k
✕
k
✕
k
✕
k
✕
l
✕
l
✕
l
✕
m
✕
m
(iii)
4
✕
k
✕
k
✕
k
✕
l
✕
l
✕
l
✕
m
✕
m
(iv)
k
✕
k
✕
l
✕
l
✕
l
✕
m
✕
m
(v)
-2
✕
k
✕
k
✕
k
✕
l
✕
l
✕
l
✕
m
✕
m
Question
20
20.
Factorize
(
x
2
+
2
x
a
+
a
2
−
16
)
(i)
(
x
+
a
+
4
)
(
x
+
a
−
4
)
(ii)
(
x
−
a
−
4
)
(
x
+
a
−
4
)
(iii)
(
x
−
a
+
4
)
(
x
+
a
+
4
)
(iv)
(
x
+
a
+
4
)
(
x
−
a
−
4
)
(v)
(
x
+
a
−
4
)
(
x
−
a
+
4
)
Question
21
21.
The quotient of
(
−
64
a
3
+
64
b
3
)
÷
(
−
4
a
+
4
b
)
is
(i)
(
15
a
2
+
16
a
b
+
16
b
2
)
(ii)
(
16
a
2
+
13
a
b
+
16
b
2
)
(iii)
(
16
a
2
+
19
a
b
+
16
b
2
)
(iv)
(
16
a
2
+
16
a
b
+
16
b
2
)
(v)
(
17
a
2
+
16
a
b
+
16
b
2
)
Question
22
22.
The quotient of
(
4
a
2
−
16
b
2
)
÷
(
−
2
a
−
4
b
)
is
(i)
(
−
a
+
4
b
)
(ii)
(
−
2
a
+
4
b
)
(iii)
(
−
3
a
+
4
b
)
(iv)
(
−
2
a
+
2
b
)
(v)
(
−
2
a
+
7
b
)
Question
23
23.
Which of the following is a factor of
48
x
y
3
z
2
?
(i)
12
x
y
2
z
3
(ii)
12
x
y
4
(iii)
x
2
y
2
(iv)
12
x
y
2
Question
24
24.
(
x
4
+
9
x
3
+
20
x
2
)
÷
(
x
2
+
5
x
)
(i)
(
x
2
+
4
x
)
(ii)
4
x
(iii)
(
−
x
2
+
4
x
)
(iv)
(
x
2
+
5
x
)
(v)
(
x
2
−
4
x
)
Question
25
25.
The quotient of
(
−
64
a
3
+
8
b
3
)
÷
(
−
4
a
+
2
b
)
is
(i)
(
15
a
2
+
8
a
b
+
4
b
2
)
(ii)
(
16
a
2
+
5
a
b
+
4
b
2
)
(iii)
(
16
a
2
+
8
a
b
+
4
b
2
)
(iv)
(
17
a
2
+
8
a
b
+
4
b
2
)
(v)
(
16
a
2
+
11
a
b
+
4
b
2
)
Assignment Key
1) (i)
2) (ii)
3) (v)
4) (iv)
5) (iii)
6) (iv)
7) (ii)
8) (iii)
9) (iv)
10) (iii)
11) (iv)
12) (ii)
13) (v)
14) (v)
15) (v)
16) (v)
17) (iv)
18) (v)
19) (i)
20) (i)
21) (iv)
22) (ii)
23) (iv)
24) (i)
25) (iii)
