EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
Factorize
(
36
x
2
−
64
y
2
)
(i)
(
6
x
−
8
y
)
(
6
x
−
8
y
)
(ii)
(
6
x
+
8
y
)
(
6
x
−
8
y
)
(iii)
(
6
x
−
2
y
)
(
6
x
+
32
y
)
(iv)
(
6
x
+
2
y
)
(
6
x
−
32
y
)
(v)
(
6
x
+
8
y
)
(
6
x
+
8
y
)
Question
2
2.
The value of
48
1
2
✕
48
1
2
is
(i)
2351
3
4
(ii)
2352
1
4
(iii)
2352
1
6
(iv)
2352
1
2
(v)
2352
3
4
Question
3
3.
Which of the following algebraic expressions is a cubic polynomial?
(i)
(
−
4
)
(ii)
(
8
t
−
6
)
(iii)
(
−
4
t
3
−
t
2
+
2
t
+
1
)
(iv)
(
t
2
+
6
t
+
2
)
(v)
(
−
9
t
5
−
6
t
3
+
7
t
2
−
4
t
−
2
)
Question
4
4.
Factorize
(
a
6
−
b
6
)
(i)
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
(ii)
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
(
a
+
b
)
(
a
2
−
a
b
−
b
2
)
(iii)
(
a
−
b
)
(
a
2
−
a
b
+
b
2
)
(
a
+
b
)
(
a
2
−
a
b
−
b
2
)
(iv)
(
a
−
b
)
(
a
2
+
a
b
−
b
2
)
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
(v)
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
(
a
+
b
)
(
a
2
+
a
b
−
b
2
)
Question
5
5.
The remainder when
(
−
2
j
2
−
6
j
−
3
)
is divided by
(
j
+
3
)
is
(i)
(
−
3
)
(ii)
(
−
2
)
(iii)
(
−
1
)
(iv)
(
−
6
)
(v)
(
−
4
)
Question
6
6.
Which of the following are true?
a)
Zero of a polynomial and zero polynomial are synonymous
b)
If (x - a) is a factor of f(x), then f(a) = 0
c)
A polynomial of degree n has atmost n zeros
d)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
e)
Zero of a polynomial and root of the polynomial are synonymous
f)
If (x + a) is a factor of f(x), then f(a) = 0
g)
A linear polynomial in one variable has only one root
(i)
{a,b}
(ii)
{b,c,d,e,g}
(iii)
{f,c}
(iv)
{a,f,d}
(v)
{a,e,g}
Question
7
7.
Which of the following algebraic expressions is a binomial?
(i)
(
9
c
4
+
8
c
2
+
c
)
(ii)
(
−
8
c
4
+
6
c
3
+
6
c
2
+
6
c
−
7
)
(iii)
9
c
3
(iv)
(
2
c
4
+
7
c
3
−
8
c
2
−
9
c
−
8
)
(v)
(
9
c
3
−
4
)
Question
8
8.
Factorize
(
a
3
+
9
a
2
b
+
27
a
b
2
+
27
b
3
)
(i)
(
2
a
+
3
b
)
(
2
a
+
3
b
)
(
2
a
+
3
b
)
(ii)
(
a
+
5
b
)
(
a
+
6
b
)
(
a
+
5
b
)
(iii)
(
a
+
3
b
)
(
a
+
3
b
)
(
a
+
3
b
)
(iv)
3
b
3
b
3
b
(v)
(
a
+
b
)
(
a
+
b
)
a
Question
9
9.
In which of the cases,
g
(
x
)
is a factor of
f
(
x
)
?
(i)
f
(
x
)
=
(
−
x
3
−
6
x
2
+
x
+
6
)
,
g
(
x
)
=
(
x
+
2
)
(ii)
f
(
x
)
=
(
x
3
+
12
x
2
+
44
x
+
48
)
,
g
(
x
)
=
(
x
+
1
)
(iii)
f
(
x
)
=
(
−
x
3
−
4
x
2
+
x
+
4
)
,
g
(
x
)
=
(
−
x
+
1
)
(iv)
f
(
x
)
=
(
x
3
+
9
x
2
+
20
x
+
12
)
,
g
(
x
)
=
(
−
3
x
+
8
)
(v)
f
(
x
)
=
(
−
3
x
3
−
16
x
2
+
28
x
+
96
)
,
g
(
x
)
=
(
x
+
4
)
Question
10
10.
(
−
54
x
4
+
63
x
3
−
12
x
2
−
7
x
+
2
)
÷
(
−
18
x
3
+
27
x
2
−
13
x
+
2
)
=
(i)
(
4
x
+
1
)
(ii)
(
3
x
+
1
)
(iii)
(
−
3
x
+
1
)
(iv)
(
2
x
+
1
)
(v)
(
3
x
−
1
)
Question
11
11.
The expanded form of
(
x
−
4
)
(
2
x
−
1
)
is
(i)
(
4
x
2
−
9
x
+
4
)
(ii)
(
−
x
2
−
9
x
+
4
)
(iii)
(
2
x
2
−
9
x
+
4
)
(iv)
(
x
2
−
9
x
+
4
)
(v)
(
3
x
2
−
9
x
+
4
)
Question
12
12.
Evaluate :
980
2
−
20
2
(i)
9600000
(ii)
960020
(iii)
960980
(iv)
96000
(v)
960000
Question
13
13.
The degree of polynomial
(
−
2
h
2
+
9
h
i
+
3
i
−
3
)
is
(i)
1
(ii)
4
(iii)
(-1)
(iv)
3
(v)
2
Question
14
14.
Factorize
(
x
4
−
5
x
3
+
5
x
2
+
5
x
−
6
)
(i)
(
x
−
1
)
(
x
−
3
)
(
x
−
2
)
(
x
+
2
)
(ii)
(
x
−
1
)
(
x
−
3
)
(
x
−
2
)
(
x
+
1
)
(iii)
(
x
−
1
)
(
x
−
3
)
(
x
−
2
)
(
x
+
3
)
(iv)
(
x
−
1
)
(
x
−
3
)
(
x
+
1
)
(
x
+
2
)
(v)
(
x
−
1
)
(
x
−
3
)
(
x
+
2
)
(
x
+
3
)
Question
15
15.
Given
f
(
i
)
=
(
−
4
i
−
1
)
,
find
f
(
1
)
(i)
-7
(ii)
-5
(iii)
-6
(iv)
-4
(v)
-2
Question
16
16.
Which of the following is a factor of
6
x
4
y
2
z
3
?
(i)
2
x
4
z
4
(ii)
2
x
2
y
3
z
3
(iii)
x
5
z
3
(iv)
2
x
2
z
4
(v)
2
x
2
z
3
Question
17
17.
(
a
+
b
+
c
)
2
(i)
(
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(ii)
(
2
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iii)
(
a
2
−
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(iv)
(
a
2
+
2
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
(v)
(
a
2
+
4
a
b
+
2
a
c
+
b
2
+
2
b
c
+
c
2
)
Question
18
18.
Factorize
(
6
x
+
9
y
)
2
−
2
(
6
x
+
9
y
)
(
3
x
+
7
y
)
+
(
3
x
+
7
y
)
2
(i)
(
9
x
+
16
y
)
2
(ii)
(
4
x
+
2
y
)
2
(iii)
(
6
x
+
9
y
)
(
3
x
+
7
y
)
(iv)
(
3
x
+
2
y
)
2
(v)
(
−
2
x
−
2
y
)
2
Question
19
19.
(
a
+
b
)
2
(i)
(
a
2
+
2
a
b
+
b
2
)
(ii)
(
a
2
−
a
b
+
b
2
)
(iii)
(
2
a
b
+
b
2
)
(iv)
(
a
2
+
4
a
b
+
b
2
)
(v)
(
2
a
2
+
2
a
b
+
b
2
)
Question
20
20.
Factorize
(
63
a
2
b
+
18
a
b
2
)
(i)
9
a
b
(
7
a
+
2
b
)
(ii)
9
a
(
7
a
+
2
b
)
(iii)
9
a
b
(
7
a
−
2
b
)
(iv)
9
a
b
(
−
7
a
−
2
b
)
(v)
9
b
(
7
a
−
2
b
)
Question
21
21.
Find the value of
9.2
3
+
3
3
−
12.2
3
(i)
-216
(ii)
-1010.16
(iii)
216
(iv)
6229.504
(v)
-6229.504
Question
22
22.
The quotient of
(
25
a
2
+
40
a
b
+
16
b
2
)
÷
(
−
5
a
−
4
b
)
is
(i)
(
−
5
a
−
4
b
)
(ii)
(
−
6
a
−
4
b
)
(iii)
(
−
5
a
−
7
b
)
(iv)
(
−
4
a
−
4
b
)
(v)
(
−
5
a
−
b
)
Question
23
23.
If the polynomial
f
(
x
)
=
k
x
2
+
3
x
−
9
is exactly divisible by
(
2
x
+
3
)
,
find
k
(i)
6
(ii)
4
(iii)
9
(iv)
5
(v)
7
Question
24
24.
(
3
2
a
+
2
3
b
)
3
(i)
(
27
8
a
3
+
11
2
a
2
b
+
2
a
b
2
+
8
27
b
3
)
(ii)
(
27
8
a
3
+
7
2
a
2
b
+
2
a
b
2
+
8
27
b
3
)
(iii)
(
33
10
a
3
+
9
2
a
2
b
+
2
a
b
2
+
8
27
b
3
)
(iv)
(
7
2
a
3
+
9
2
a
2
b
+
2
a
b
2
+
8
27
b
3
)
(v)
(
27
8
a
3
+
9
2
a
2
b
+
2
a
b
2
+
8
27
b
3
)
Question
25
25.
Factorize
(
6
x
2
+
6
x
y
−
12
y
2
)
(i)
(
3
x
−
6
y
)
(
2
x
−
2
y
)
(ii)
(
3
x
+
6
y
)
(
2
x
+
2
y
)
(iii)
(
3
x
+
6
y
)
(
2
x
−
2
y
)
(iv)
(
3
x
−
6
y
)
(
2
x
+
2
y
)
(v)
(
3
x
+
6
y
)
(
3
x
−
6
y
)
Assignment Key
1) (ii)
2) (ii)
3) (iii)
4) (i)
5) (i)
6) (ii)
7) (v)
8) (iii)
9) (iii)
10) (ii)
11) (iii)
12) (v)
13) (v)
14) (ii)
15) (ii)
16) (v)
17) (iv)
18) (iv)
19) (i)
20) (i)
21) (ii)
22) (i)
23) (i)
24) (v)
25) (iii)
