EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Find the table of points that satisfy
the parabola equation
y
=
2
x
2
(i)
x
-2
-1
-2
1
2
y
8
2
-2
2
8
(ii)
x
-2
-1
0
0
2
y
8
2
0
3
8
(iii)
x
-2
-1
0
1
2
y
8
2
0
2
8
(iv)
x
-2
-1
1
1
2
y
8
2
-1
2
8
(v)
x
-2
-1
0
1
4
y
8
2
0
2
10
Question
2
2.
The degree of the polynomial
(
−
8
w
−
1
)
is
(i)
2
(ii)
(-1)
(iii)
0
(iv)
1
(v)
3
Question
3
3.
Find the quadratic equation, the sum of whose roots is
(
-3
5
)
and product is
(
-2
5
)
(i)
(
26
x
2
+
15
x
−
10
)
=
0
(ii)
(
25
x
2
+
17
x
−
10
)
=
0
(iii)
(
25
x
2
+
12
x
−
10
)
=
0
(iv)
(
24
x
2
+
15
x
−
10
)
=
0
(v)
(
25
x
2
+
15
x
−
10
)
=
0
Question
4
4.
Find the quadratic equation with roots
(
8
,
-5
)
(i)
(
x
2
−
4
x
−
32
)
=
0
(ii)
(
x
2
−
3
x
−
40
)
=
0
(iii)
(
x
2
−
6
x
−
16
)
=
0
(iv)
(
x
2
−
25
)
=
0
(v)
(
x
2
−
2
x
−
35
)
=
0
Question
5
5.
Find the quadratic equation, the sum of whose roots is
-4
and product is
-5
(i)
(
4
x
−
5
)
=
0
(ii)
(
x
2
+
2
x
−
5
)
=
0
(iii)
(
2
x
2
+
4
x
−
5
)
=
0
(iv)
(
x
2
+
4
x
−
5
)
=
0
(v)
(
x
2
+
7
x
−
5
)
=
0
Question
6
6.
Factorize and divide
(
16
x
4
−
436
x
2
+
900
)
÷
(
4
x
2
−
14
x
−
30
)
(i)
(
7
x
2
+
14
x
−
30
)
(ii)
(
5
x
2
+
14
x
−
30
)
(iii)
(
4
x
2
+
14
x
−
30
)
(iv)
(
x
2
+
14
x
−
30
)
(v)
(
3
x
2
+
14
x
−
30
)
Question
7
7.
The degree of the polynomial
(
6
n
5
+
8
n
4
+
7
n
3
−
3
n
2
−
3
n
)
is
(i)
6
(ii)
8
(iii)
4
(iv)
2
(v)
5
Question
8
8.
Which of the displayed parabolae represent
the equation
y
=
2
x
2
(i)
parabola with point
K
(ii)
parabola with point
M
(iii)
parabola with point
L
(iv)
parabola with point
N
Question
9
9.
If the polynomial
2
x
4
−
5
x
3
−
57
x
2
+
a
x
+
b
is divided by
(
x
−
6
)
,
it leaves a remainder
648
.
If it is divided by
(
x
−
4
)
,
it leaves a remainder
0
.
Find the value of
a
and
b
(i)
234
,
-215
(ii)
235
,
-216
(iii)
-215
,
235
(iv)
234
,
-216
(v)
-217
,
233
Question
10
10.
Find the table of points that satisfy
the parabola equation
y
=
(
x
2
+
8
x
+
16
)
(i)
x
-2
-1
0
0
2
y
4
9
16
26
36
(ii)
x
-2
-1
1
1
2
y
4
9
15
25
36
(iii)
x
-2
-1
0
1
4
y
4
9
16
25
38
(iv)
x
-2
-1
0
1
2
y
4
9
16
25
36
(v)
x
-2
-1
-2
1
2
y
4
9
14
25
36
Question
11
11.
If the polynomials
a
x
2
−
x
+
23
and
−
2
x
2
+
a
x
+
3
leave the same remainder when divided by
(
x
+
2
)
,
find the value of
a
(i)
(-2)
(ii)
(-7)
(iii)
(-4)
(iv)
(-5)
(v)
(-6)
Question
12
12.
The degree of the polynomial
(
−
5
h
4
+
5
h
3
−
h
2
)
is
(i)
4
(ii)
3
(iii)
5
(iv)
7
(v)
1
Question
13
13.
Which of the following algebraic expressions is a linear polynomial?
(i)
(
7
x
+
2
)
(ii)
(
−
9
x
5
−
5
x
4
+
5
x
3
+
4
x
2
−
6
)
(iii)
6
(iv)
(
−
8
x
2
−
6
x
+
2
)
(v)
(
9
x
3
−
2
x
2
+
4
x
−
4
)
Question
14
14.
If
5
and
-2
are the zeros of the polynomial
f
(
x
)
=
b
x
4
−
18
x
3
−
22
x
2
+
a
x
, find the value of
a
and
b
(i)
3
,
59
(ii)
5
,
61
(iii)
61
,
4
(iv)
60
,
5
(v)
60
,
4
Question
15
15.
If
1
is the zero of the polynomial
f
(
x
)
=
3
x
2
+
k
x
+
6
,
find
k
(i)
-12
(ii)
-10
(iii)
-9
(iv)
-6
(v)
-8
Question
16
16.
The remainder when
9
r
2
is divided by
(
r
−
2
)
is
(i)
38
(ii)
33
(iii)
37
(iv)
36
(v)
35
Question
17
17.
Which of the displayed parabolae represents
the equation
y
=
(
x
2
+
12
x
+
35
)
(i)
parabola with point
L
(ii)
parabola with point
M
(iii)
parabola with point
N
(iv)
parabola with point
O
Question
18
18.
Which of the following algebraic expressions is a quadratic polynomial?
(i)
(
−
9
e
−
6
)
(ii)
(
7
e
3
−
9
e
2
+
6
e
−
2
)
(iii)
(
−
e
2
−
9
e
+
7
)
(iv)
4
(v)
(
2
e
5
+
2
e
4
−
2
e
3
−
9
e
−
1
)
Question
19
19.
Find the roots of the quadratic equation
(
x
2
−
11
x
+
18
)
=
0
(i)
(
10
,
2
)
(ii)
(
10
,
1
)
(iii)
(
12
,
1
)
(iv)
(
12
,
0
)
(v)
(
9
,
2
)
Question
20
20.
The quotient when
(
4
x
5
+
8
x
4
−
7
x
3
−
9
x
2
−
4
x
+
1
)
is divided by
(
x
+
7
)
is
(i)
(
x
4
−
20
x
3
+
133
x
2
−
940
x
+
6576
)
(ii)
(
4
x
4
−
20
x
3
+
133
x
2
−
940
x
+
6576
)
(iii)
(
7
x
4
−
20
x
3
+
133
x
2
−
940
x
+
6576
)
(iv)
(
3
x
4
−
20
x
3
+
133
x
2
−
940
x
+
6576
)
(v)
(
5
x
4
−
20
x
3
+
133
x
2
−
940
x
+
6576
)
Question
21
21.
The remainder when
(
7
j
2
−
8
j
)
is divided by
(
j
+
7
)
is
(i)
396
(ii)
402
(iii)
399
(iv)
398
(v)
400
Question
22
22.
Find the value of
a
and
b
such that
a
x
4
−
x
3
+
b
x
2
+
60
x
is exactly divisible by
(
x
2
+
x
−
20
)
(i)
-42
,
3
(ii)
2
,
-42
(iii)
2
,
-43
(iv)
3
,
-43
(v)
-44
,
1
Question
23
23.
(
−
18
x
5
+
9
x
4
+
126
x
3
+
72
x
2
−
108
x
−
81
)
divided by
(
−
3
x
3
+
9
x
2
+
3
x
−
9
)
=
(i)
(
6
x
2
+
15
x
−
9
)
(ii)
(
6
x
2
−
15
x
+
9
)
(iii)
(
6
x
2
+
15
x
+
9
)
(iv)
(
6
x
2
+
16
x
+
9
)
(v)
(
6
x
2
+
14
x
+
9
)
Question
24
24.
Given
f
(
z
)
=
(
−
6
z
2
−
8
z
−
3
)
,
find
f
(
4
)
(i)
-130
(ii)
-131
(iii)
-133
(iv)
-129
(v)
-132
Question
25
25.
Find the quadratic polynomial which when divided by
(
3
x
−
5
)
,
(
3
x
+
7
)
,
(
3
x
−
7
)
leaves remainders of
65
9
,
725
9
,
11
9
respectively.
(i)
(
2
x
2
−
17
x
+
30
)
(ii)
(
9
x
2
−
49
)
(iii)
(
6
x
2
−
29
x
+
35
)
(iv)
(
3
x
2
−
23
x
+
30
)
(v)
(
9
x
2
+
6
x
−
35
)
Assignment Key
1) (iii)
2) (iv)
3) (v)
4) (ii)
5) (iv)
6) (iii)
7) (v)
8) (i)
9) (iv)
10) (iv)
11) (iv)
12) (i)
13) (i)
14) (v)
15) (iii)
16) (iv)
17) (iii)
18) (iii)
19) (v)
20) (ii)
21) (iii)
22) (iii)
23) (iii)
24) (ii)
25) (i)
