EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Factorisation
Grade : ICSE Grade VII
License : Non Commercial Use
Question
1
1.
Factorize
(
x
2
+
14
x
+
45
)
(i)
(
x
−
9
)
(
x
−
5
)
(ii)
(
x
+
9
)
(
x
+
5
)
(iii)
(
x
+
9
)
(
x
−
5
)
(iv)
(
x
−
9
)
(
x
+
5
)
Question
2
2.
Factorize
4
a
3
−
36
a
(i)
(
2
a
+
6
)
(
6
a
−
2
)
a
(ii)
(
2
a
+
6
)
(
2
a
2
+
6
)
a
(iii)
(
2
a
+
6
)
(
2
a
−
6
)
a
(iv)
(
2
a
2
+
6
)
(
6
a
−
2
)
a
(v)
(
2
a
−
6
)
(
2
a
2
+
6
)
a
Question
3
3.
Which of the following are true?
a)
Degree of zero polynomial is zero
b)
π
r
2
is a monomial
c)
A binomial has two and only two terms
d)
A binomial may have degree 3
e)
Every polynomial is a binomial
(i)
{a,b,c}
(ii)
{e,c}
(iii)
{a,e,d}
(iv)
{b,c,d}
(v)
{a,b}
Question
4
4.
Factorize
a
2
c
2
−
b
2
c
2
−
a
2
d
2
+
b
2
d
2
(i)
(
a
+
b
)
(
a
−
b
)
(
c
+
d
)
(
b
−
d
)
(ii)
(
a
+
b
)
(
a
−
c
)
(
c
+
d
)
(
c
−
d
)
(iii)
(
a
+
c
)
(
a
−
c
)
(
b
+
d
)
(
b
−
d
)
(iv)
(
a
+
b
)
(
a
−
b
)
(
b
+
d
)
(
c
−
d
)
(v)
(
a
+
b
)
(
a
−
b
)
(
c
+
d
)
(
c
−
d
)
Question
5
5.
Factorize
(
a
x
+
b
y
)
2
−
(
a
x
−
b
y
)
2
(i)
4
a
x
b
y
(ii)
2
(
a
x
)
2
(
b
y
)
2
(iii)
4
(
a
x
)
2
(
b
y
)
2
(iv)
2
a
x
b
y
Question
6
6.
Factorize
(
16
a
2
b
+
14
a
b
2
)
(i)
2
a
b
(
8
a
−
7
b
)
(ii)
2
b
(
8
a
−
7
b
)
(iii)
2
a
b
(
8
a
+
7
b
)
(iv)
2
a
(
8
a
+
7
b
)
(v)
2
a
b
(
−
8
a
−
7
b
)
Question
7
7.
Factorize
(
49
x
2
−
64
y
2
)
(i)
(
7
x
+
32
y
)
(
7
x
−
2
y
)
(ii)
(
7
x
+
8
y
)
(
7
x
+
8
y
)
(iii)
(
7
x
+
8
y
)
(
7
x
−
8
y
)
(iv)
(
7
x
−
8
y
)
(
7
x
−
8
y
)
(v)
(
7
x
−
32
y
)
(
7
x
+
2
y
)
Question
8
8.
Factorize
a
2
−
b
2
−
c
2
−
2
b
c
(i)
(
a
+
b
+
c
)
(
a
+
b
−
c
)
(ii)
(
a
−
b
−
c
)
(
a
+
b
−
c
)
(iii)
(
a
−
b
−
c
)
(
a
−
b
+
c
)
(iv)
(
a
+
b
+
c
)
(
a
−
b
+
c
)
(v)
(
a
−
b
−
c
)
(
a
+
b
+
c
)
Question
9
9.
Find the H.C.F. of
228
x
2
y
2
z
3
and
36
x
3
y
z
3
(i)
684
x
3
y
2
z
3
(ii)
12
x
3
y
z
3
(iii)
12
x
2
y
3
z
3
(iv)
12
x
2
y
z
3
(v)
12
x
2
y
z
5
Question
10
10.
Find the H.C.F. of
40
x
and
152
x
3
(i)
760
x
3
(ii)
8
x
4
(iii)
8
x
3
(iv)
8
x
2
(v)
8
x
Question
11
11.
Factorize
(
6
x
2
−
25
x
+
25
)
(i)
(
2
x
−
5
)
(
3
x
−
5
)
(ii)
(
2
x
−
5
)
(
2
x
−
5
)
(iii)
(
2
x
−
5
)
(
5
x
−
5
)
(iv)
(
2
x
−
5
)
(
4
x
−
5
)
(v)
(
2
x
−
5
)
(
x
−
5
)
Question
12
12.
Find the H.C.F. of
(
x
2
−
x
−
12
)
and
(
x
2
+
5
x
+
6
)
(i)
(
x
−
4
)
(ii)
(
x
+
3
)
(iii)
(
x
+
2
)
(iv)
(
2
x
+
3
)
(v)
(
2
x
−
4
)
Question
13
13.
Factorize
(
a
+
b
)
2
−
c
2
(i)
(
a
+
b
+
c
)
(
a
−
b
+
c
)
(ii)
(
a
+
b
+
c
)
(
a
+
b
−
c
)
(iii)
(
a
+
b
−
c
)
(
a
−
b
−
c
)
(iv)
(
a
+
b
−
c
)
(
a
−
b
+
c
)
(v)
(
a
+
b
+
c
)
(
a
−
b
−
c
)
Question
14
14.
Factorize
(
25
a
2
−
40
a
b
+
50
a
c
+
16
b
2
−
40
b
c
+
25
c
2
)
(i)
(
4
a
−
4
b
+
5
c
)
(
4
a
−
4
b
+
5
c
)
(ii)
(
5
a
−
6
b
+
5
c
)
(
5
a
−
7
b
+
5
c
)
(iii)
(
5
a
−
b
+
5
c
)
(
5
a
−
2
b
+
5
c
)
(iv)
(
6
a
−
4
b
+
5
c
)
(
6
a
−
4
b
+
5
c
)
(v)
(
5
a
−
4
b
+
5
c
)
(
5
a
−
4
b
+
5
c
)
Question
15
15.
Factorize
a
2
b
2
−
b
2
c
2
(i)
(
a
b
+
b
c
)
(
a
b
−
b
c
)
(ii)
(
a
b
+
b
c
)
(
a
c
+
b
c
)
(iii)
(
a
b
−
b
c
)
(
a
b
−
b
c
)
(iv)
(
a
c
+
b
c
)
(
a
c
−
b
c
)
(v)
(
a
b
+
b
c
)
(
a
b
+
b
c
)
Question
16
16.
Factorize
(
3
x
+
7
y
)
2
−
2
(
3
x
+
7
y
)
(
8
x
+
6
y
)
+
(
8
x
+
6
y
)
2
(i)
(
11
x
+
13
y
)
2
(ii)
(
6
x
−
y
)
2
(iii)
(
−
4
x
+
y
)
2
(iv)
(
3
x
+
7
y
)
(
8
x
+
6
y
)
(v)
(
−
5
x
+
y
)
2
Question
17
17.
Which of the following gives the H.C.F of two or more polynomials?
(i)
( H.C.F. of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
(ii)
( Product of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
(iii)
( Product of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
(iv)
( H.C.F. of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
Question
18
18.
Find the number of numbers between
8
2
and
9
2
(i)
13
(ii)
16
(iii)
15
(iv)
17
(v)
19
Question
19
19.
Which of the following is an irreducible factor of
19
x
y
3
z
5
?
(i)
x
2
y
3
z
4
(ii)
x
2
y
(iii)
x
z
4
(iv)
y
3
z
(v)
x
Question
20
20.
Factorize
(
25
a
2
−
4
b
2
)
(i)
(
5
a
−
2
b
)
(
5
a
+
2
b
)
(ii)
(
6
a
−
2
b
)
(
6
a
+
2
b
)
(iii)
(
4
a
−
2
b
)
(
4
a
+
2
b
)
(iv)
(
5
a
−
4
b
)
(
5
a
−
b
)
(v)
5
a
(
5
a
+
5
b
)
Question
21
21.
Factorize
(
x
2
+
2
x
a
−
x
+
a
2
−
a
−
20
)
(i)
(
x
+
a
+
4
)
(
x
+
a
−
5
)
(ii)
(
x
−
a
+
4
)
(
x
+
a
+
5
)
(iii)
(
x
−
a
−
5
)
(
x
+
a
−
4
)
(iv)
(
x
+
a
−
5
)
(
x
−
a
+
4
)
(v)
(
x
+
a
+
4
)
(
x
−
a
−
5
)
Question
22
22.
Factorize
(
x
4
−
13
x
3
+
41
x
2
+
13
x
−
42
)
(i)
(
x
−
7
)
(
4
x
−
6
)
(
4
x
+
1
)
(
3
x
−
1
)
(ii)
(
x
−
7
)
(
2
x
−
6
)
(
2
x
+
1
)
(
2
x
−
1
)
(iii)
(
x
−
7
)
(
x
−
6
)
(
x
+
1
)
(
x
−
1
)
(iv)
(
x
−
7
)
(
−
6
)
1
(
−
1
)
(v)
(
x
−
7
)
(
−
x
−
6
)
(
−
x
+
1
)
(
−
2
x
−
1
)
Question
23
23.
Which of the following is a factor of
(
3
x
5
+
y
4
z
2
)
?
(i)
3
y
(ii)
no factors
(iii)
3
x
5
(iv)
y
4
z
2
(v)
3
x
4
z
2
Question
24
24.
Factorize
(
4
x
3
−
8
x
2
−
41
x
−
18
)
(i)
(
2
x
+
1
)
(
2
x
−
9
)
(
x
+
2
)
(ii)
(
2
x
+
1
)
(
3
x
−
9
)
(
2
x
+
2
)
(iii)
(
2
x
+
1
)
(
x
−
9
)
2
(iv)
(
2
x
+
1
)
(
4
x
−
9
)
(
3
x
+
2
)
(v)
(
2
x
+
1
)
(
−
9
)
(
−
x
+
2
)
Question
25
25.
Factorize
(
16
a
2
+
32
a
b
+
16
b
2
)
(i)
(
4
a
+
2
b
)
(
4
a
+
b
)
(ii)
(
4
a
+
6
b
)
(
4
a
+
6
b
)
(iii)
(
3
a
+
4
b
)
(
3
a
+
4
b
)
(iv)
(
5
a
+
4
b
)
(
5
a
+
4
b
)
(v)
(
4
a
+
4
b
)
(
4
a
+
4
b
)
Assignment Key
1) (ii)
2) (iii)
3) (iv)
4) (v)
5) (i)
6) (iii)
7) (iii)
8) (v)
9) (iv)
10) (v)
11) (i)
12) (ii)
13) (ii)
14) (v)
15) (i)
16) (v)
17) (iv)
18) (ii)
19) (v)
20) (i)
21) (i)
22) (iii)
23) (ii)
24) (i)
25) (v)
