EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
Which of the following algebraic expressions is a monomial?
(i)
(
−
9
r
4
+
7
r
3
−
4
r
2
−
2
r
−
6
)
(ii)
3
r
3
(iii)
(
−
6
r
4
+
7
r
3
−
r
2
−
3
r
−
8
)
(iv)
(
8
r
3
−
8
r
2
−
9
r
)
(v)
(
8
r
2
+
7
)
Question
2
2.
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)
Zero of a polynomial and root of the polynomial are synonymous
d)
If (x - a) is a factor of f(x), then f(a) = 0
e)
A linear polynomial in one variable has only one root
f)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
g)
A polynomial of degree n has atmost n zeros
(i)
{b,d}
(ii)
{c,d,e,f,g}
(iii)
{a,c}
(iv)
{a,b,e}
(v)
{a,f,g}
Question
3
3.
If
5
and
-4
are the zeros of the polynomial
f
(
x
)
=
2
x
4
+
b
x
3
+
a
x
2
+
96
x
+
320
, find the value of
a
and
b
(i)
-52
,
-5
(ii)
-51
,
-6
(iii)
-52
,
-6
(iv)
-7
,
-53
(v)
-5
,
-51
Question
4
4.
Which of the following are possible values
for the length and breadth of a rectangle
whose area is
(
−
8
x
2
−
18
x
+
18
)
(i)
(
−
3
x
+
2
)
(
2
x
−
6
)
(ii)
(
−
4
x
−
3
)
(
2
x
−
6
)
(iii)
(
−
4
x
−
3
)
(
2
x
+
6
)
(iv)
(
−
4
x
+
3
)
(
2
x
−
6
)
(v)
(
−
4
x
+
3
)
(
2
x
+
6
)
Question
5
5.
(
−
2
a
−
2
3
b
+
2
c
)
2
(i)
(
5
a
2
+
8
3
a
b
−
8
a
c
+
4
9
b
2
−
8
3
b
c
+
4
c
2
)
(ii)
(
3
a
2
+
8
3
a
b
−
8
a
c
+
4
9
b
2
−
8
3
b
c
+
4
c
2
)
(iii)
(
4
a
2
+
8
3
a
b
−
8
a
c
+
4
9
b
2
−
8
3
b
c
+
4
c
2
)
(iv)
(
4
a
2
+
2
a
b
−
8
a
c
+
4
9
b
2
−
8
3
b
c
+
4
c
2
)
(v)
(
4
a
2
+
10
3
a
b
−
8
a
c
+
4
9
b
2
−
8
3
b
c
+
4
c
2
)
Question
6
6.
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
7
7.
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
8
8.
The constant term in polynomial
(
−
9
h
3
+
4
h
2
−
6
h
−
1
)
is
(i)
-2
(ii)
0
(iii)
1
(iv)
-1
(v)
-4
Question
9
9.
Factorize
(
16
a
2
−
4
b
2
)
(i)
(
4
a
+
2
b
)
(
4
a
−
2
b
)
(ii)
(
4
a
+
5
b
)
(
4
a
+
b
)
(iii)
(
3
a
+
2
b
)
(
3
a
−
2
b
)
(iv)
(
5
a
+
2
b
)
(
5
a
−
2
b
)
(v)
4
a
(
4
a
−
4
b
)
Question
10
10.
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
11
11.
If
f
(
x
)
=
(
9
x
3
+
33
x
2
−
18
x
−
24
)
and
g
(
x
)
=
(
18
x
3
−
48
x
2
+
8
x
+
32
)
have a common factor, find the common factor
(i)
(
x
+
4
)
(ii)
(
3
x
+
2
)
(iii)
(
2
x
−
4
)
(iv)
(
3
x
−
4
)
(v)
(
3
x
−
3
)
Question
12
12.
The quotient of
(
4
a
2
−
12
a
b
+
9
b
2
)
÷
(
−
2
a
+
3
b
)
is
(i)
(
−
a
+
3
b
)
(ii)
(
−
2
a
+
5
b
)
(iii)
(
−
3
a
+
3
b
)
(iv)
(
−
2
a
+
3
b
)
(v)
(
−
2
a
)
Question
13
13.
The value of the polynomial
(
−
4
s
4
+
4
s
3
−
6
s
2
+
7
s
+
5
)
at
s
=
(-1)
is
(i)
-19
(ii)
-17
(iii)
-14
(iv)
-15
(v)
-16
Question
14
14.
(
−
5
a
−
3
b
+
4
c
)
2
(i)
(
25
a
2
+
28
a
b
−
40
a
c
+
9
b
2
−
24
b
c
+
16
c
2
)
(ii)
(
25
a
2
+
30
a
b
−
40
a
c
+
9
b
2
−
24
b
c
+
16
c
2
)
(iii)
(
24
a
2
+
30
a
b
−
40
a
c
+
9
b
2
−
24
b
c
+
16
c
2
)
(iv)
(
25
a
2
+
32
a
b
−
40
a
c
+
9
b
2
−
24
b
c
+
16
c
2
)
(v)
(
26
a
2
+
30
a
b
−
40
a
c
+
9
b
2
−
24
b
c
+
16
c
2
)
Question
15
15.
Which of the following is a factor of
41
x
3
y
2
z
?
(i)
41
x
3
y
z
2
(ii)
x
4
y
z
(iii)
41
x
3
y
z
(iv)
41
x
3
y
3
z
Question
16
16.
Factorize
(
x
4
−
3
x
3
−
20
x
2
+
48
x
+
64
)
(i)
(
x
−
4
)
(
x
+
1
)
(
x
−
4
)
(
x
+
4
)
(ii)
(
x
−
4
)
(
2
x
+
1
)
(
2
x
−
4
)
(
2
x
+
4
)
(iii)
(
x
−
4
)
1
(
−
4
)
4
(iv)
(
x
−
4
)
(
−
x
+
1
)
(
−
x
−
4
)
(
−
2
x
+
4
)
(v)
(
x
−
4
)
(
3
x
+
1
)
(
3
x
−
4
)
(
3
x
+
4
)
Question
17
17.
Find
292
3
(i)
24897078
(ii)
24897088
(iii)
24897098
(iv)
24897068
(v)
24897108
Question
18
18.
Factorize
(
144
x
2
−
81
)
(i)
(
12
x
+
9
)
(
12
x
+
9
)
(ii)
(
12
x
+
9
)
(
12
x
−
9
)
(iii)
(
12
x
−
9
)
(
12
x
−
9
)
(iv)
(
12
x
+
27
)
(
12
x
−
3
)
(v)
(
12
x
−
27
)
(
12
x
+
3
)
Question
19
19.
The expanded form of
(
x
+
1
)
(
2
x
−
3
)
(
2
x
−
1
)
is
(i)
(
5
x
3
−
4
x
2
−
5
x
+
3
)
(ii)
(
2
x
3
−
4
x
2
−
5
x
+
3
)
(iii)
(
7
x
3
−
4
x
2
−
5
x
+
3
)
(iv)
(
4
x
3
−
4
x
2
−
5
x
+
3
)
(v)
(
3
x
3
−
4
x
2
−
5
x
+
3
)
Question
20
20.
The expanded form of
(
2
x
+
6
)
(
3
x
−
4
)
is
(i)
(
3
x
2
+
10
x
−
24
)
(ii)
(
7
x
2
+
10
x
−
24
)
(iii)
(
5
x
2
+
10
x
−
24
)
(iv)
(
8
x
2
+
10
x
−
24
)
(v)
(
6
x
2
+
10
x
−
24
)
Question
21
21.
The degree of polynomial
(
−
4
u
2
v
w
2
+
5
u
v
2
w
−
9
v
−
7
w
2
+
2
w
)
is
(i)
2
(ii)
6
(iii)
4
(iv)
8
(v)
5
Question
22
22.
The degree of the polynomial
(
−
6
x
4
+
7
x
3
−
5
x
2
)
is
(i)
1
(ii)
3
(iii)
7
(iv)
4
(v)
5
Question
23
23.
Factorize
25
a
3
−
16
a
(i)
(
5
a
+
4
)
(
5
a
−
4
)
a
(ii)
(
5
a
2
+
4
)
(
4
a
−
5
)
a
(iii)
(
5
a
+
4
)
(
5
a
2
+
4
)
a
(iv)
(
5
a
+
4
)
(
4
a
−
5
)
a
(v)
(
5
a
−
4
)
(
5
a
2
+
4
)
a
Question
24
24.
Given
f
(
y
)
=
(
2
y
4
+
2
y
3
+
3
y
2
−
8
y
−
6
)
,
find
f
(
(-2)
)
(i)
40
(ii)
39
(iii)
38
(iv)
36
(v)
37
Question
25
25.
The quotient of
(
9
a
2
−
6
a
b
+
b
2
)
÷
(
−
3
a
+
b
)
is
(i)
(
−
3
a
+
b
)
(ii)
(
−
3
a
−
2
b
)
(iii)
(
−
3
a
+
3
b
)
(iv)
(
−
4
a
+
b
)
(v)
(
−
2
a
+
b
)
Assignment Key
1) (ii)
2) (ii)
3) (iii)
4) (v)
5) (iii)
6) (iii)
7) (v)
8) (iv)
9) (i)
10) (i)
11) (ii)
12) (iv)
13) (v)
14) (ii)
15) (iii)
16) (i)
17) (ii)
18) (ii)
19) (iv)
20) (v)
21) (v)
22) (iv)
23) (i)
24) (iii)
25) (i)
