EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Polynomials
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
The remainder when
(
−
7
f
2
+
2
f
)
is divided by
(
f
+
5
)
is
(i)
(
−
186
)
(ii)
(
−
187
)
(iii)
(
−
185
)
(iv)
(
−
184
)
(v)
(
−
183
)
Question
2
2.
Which of the following are not polynomials?
a)
(
2
x
−
11
y
)
b)
(
2
x
2
+
3
x
y
−
77
y
2
)
c)
√x
d)
(
x
+
7
y
)
(
2
x
−
11
y
)
e)
64
x
2
(i)
{b,d}
(ii)
{e,a,c}
(iii)
{c,d}
(iv)
{b,d,c}
(v)
{a,c}
Question
3
3.
Find the quadratic equation whose roots are
(
9
+
5
√
7
)
and
(
9
−
5
√
7
)
(i)
(
2
x
2
−
18
x
−
94
)
=
0
(ii)
(
x
2
−
18
x
−
94
)
=
0
(iii)
(
−
18
x
−
94
)
=
0
(iv)
(
x
2
−
21
x
−
94
)
=
0
(v)
(
x
2
−
15
x
−
94
)
=
0
Question
4
4.
The remainder when
(
3
j
+
1
)
is divided by
(
j
−
3
)
is
(i)
9
(ii)
10
(iii)
8
(iv)
11
(v)
13
Question
5
5.
If one of the roots of the cubic equation
(
147
x
3
−
490
x
2
+
373
x
−
70
)
=
0
is
5
7
,
find the remaining real roots
(i)
(
3
7
,
0
)
(ii)
(
2
7
,
7
3
)
(iii)
(
1
,
2
5
)
(iv)
(
5
9
,
2
9
)
(v)
(
1
,
4
7
)
Question
6
6.
Given
f
(
x
)
=
(
3
x
3
−
4
x
2
+
7
x
)
,
find
f
(
(-4)
)
(i)
-287
(ii)
-281
(iii)
-283
(iv)
-285
(v)
-284
Question
7
7.
(
32
x
4
y
3
+
16
x
3
y
3
)
÷
4
x
2
y
=
(i)
(
8
x
2
y
2
+
4
y
3
)
(ii)
(
8
x
3
y
3
+
4
x
y
2
)
(iii)
(
8
x
2
y
2
+
4
x
y
3
z
)
(iv)
(
8
x
2
y
2
+
4
x
y
2
)
(v)
(
8
x
3
y
4
+
4
x
y
2
)
Question
8
8.
If
(
x
2
−
1
)
is a factor of
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
,
which of the following are true ?
a)
a + b + c = d + e
b)
a + b + c = 0
c)
b + d = 0
d)
d + e = 0
e)
a + b + c + d + e = 0
f)
a + c + e = 0
(i)
{b,c,e}
(ii)
{a,c}
(iii)
{c,e,f}
(iv)
{d,a,f}
(v)
{b,e}
Question
9
9.
Which of the following equations represents the given graph ?
(i)
y
=
(
5
x
2
+
12
x
+
5
)
(ii)
y
=
(
4
x
2
+
14
x
+
5
)
(iii)
y
=
(
3
x
2
+
12
x
+
5
)
(iv)
y
=
(
4
x
2
+
10
x
+
5
)
(v)
y
=
(
4
x
2
+
12
x
+
5
)
Question
10
10.
Which of the following is not an irreducible factor of
(
x
2
y
+
x
y
2
+
x
y
)
?
(i)
(
x
+
y
+
1
)
(ii)
x
(iii)
x
y
(iv)
y
Question
11
11.
If the polynomials
a
x
2
+
4
x
+
9
and
3
x
2
+
a
x
−
7
leave the same remainder when divided by
(
x
−
2
)
,
find the value of
a
(i)
(-9)
(ii)
(-6)
(iii)
(-7)
(iv)
(-5)
(v)
(-4)
Question
12
12.
Find the quadratic polynomial which when divided by
(
x
−
6
)
,
(
3
x
+
4
)
,
(
3
x
−
7
)
leaves remainders of
85
,
(
−
49
9
)
,
116
9
respectively.
(i)
(
9
x
2
−
9
x
−
28
)
(ii)
(
x
2
−
7
x
+
6
)
(iii)
(
3
x
2
−
14
x
−
24
)
(iv)
(
6
x
2
+
x
−
35
)
(v)
(
2
x
2
+
3
x
−
5
)
Question
13
13.
The remainder when
(
9
v
2
−
9
v
−
4
)
is divided by
(
v
−
7
)
is
(i)
373
(ii)
377
(iii)
372
(iv)
375
(v)
374
Question
14
14.
If
α
=
5
8
,
β
=
4
9
,
γ
=
4
5
are the roots of the cubic equation
a
x
3
+
b
x
2
+
c
x
+
d
= 0
,
then find
c
a
(i)
(
−
17
15
)
(ii)
2
9
(iii)
(
−
2
9
)
(iv)
(
−
673
360
)
(v)
17
15
Question
15
15.
Find the quadratic equation, the sum of whose roots is
6
and product is
9
(i)
(
2
x
2
−
6
x
+
9
)
=
0
(ii)
(
x
2
−
3
x
+
9
)
=
0
(iii)
(
x
2
−
8
x
+
9
)
=
0
(iv)
(
x
2
−
6
x
+
9
)
=
0
(v)
(
−
6
x
+
9
)
=
0
Question
16
16.
Factorize and divide
(
36
x
4
−
229
x
2
+
25
)
÷
(
6
x
2
−
13
x
−
5
)
(i)
(
5
x
2
+
13
x
−
5
)
(ii)
(
6
x
2
+
13
x
−
5
)
(iii)
(
7
x
2
+
13
x
−
5
)
(iv)
(
3
x
2
+
13
x
−
5
)
(v)
(
8
x
2
+
13
x
−
5
)
Question
17
17.
The quotient when
4
w
2
is divided by
(
w
−
8
)
is
(i)
(
5
w
+
32
)
(ii)
(
3
w
+
32
)
(iii)
(
6
w
+
32
)
(iv)
(
w
+
32
)
(v)
(
4
w
+
32
)
Question
18
18.
Which of the following are true?
a)
The curve of a parabola
is a
straight line
b)
The curve of a parabola
is a
circle
c)
The curve of a parabola
lie in only one quadrant
d)
The curve of a parabola
is a closed figure
e)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
always croses the X-axis
f)
The curve of a parabola
is a
curve
(i)
{a,f}
(ii)
{c,d,f}
(iii)
{b,f}
(iv)
{f}
(v)
{e,f}
Question
19
19.
Find the roots of the quadratic equation
(
x
2
−
6
x
+
9
)
=
0
(i)
(
4
,
3
)
(ii)
(
3
,
3
)
(iii)
(
6
,
3
)
(iv)
(
4
,
4
)
(v)
no real roots
Question
20
20.
The quotient when
(
−
9
c
2
−
4
c
)
is divided by
(
c
+
9
)
is
(i)
(
−
7
c
+
77
)
(ii)
(
−
8
c
+
77
)
(iii)
(
−
10
c
+
77
)
(iv)
(
−
11
c
+
77
)
(v)
(
−
9
c
+
77
)
Question
21
21.
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
1
2
y
8
2
0
2
8
(iii)
x
-2
-1
0
1
4
y
8
2
0
2
10
(iv)
x
-2
-1
1
1
2
y
8
2
-1
2
8
(v)
x
-2
-1
0
0
2
y
8
2
0
3
8
Question
22
22.
The sum of the roots of the quadratic equation
(
81
x
2
+
108
x
+
36
)
=
0
is
(i)
(
-6
5
)
(ii)
-2
(iii)
(
-2
3
)
(iv)
(
-4
3
)
Question
23
23.
Which of the following are true?
a)
Degree of zero polynomial is zero
b)
π
r
2
is a monomial
c)
Every polynomial is a binomial
d)
A binomial has two and only two terms
e)
A binomial may have degree 3
(i)
{c,d}
(ii)
{b,d,e}
(iii)
{a,c,e}
(iv)
{a,b}
(v)
{a,b,d}
Question
24
24.
If the polynomial
b
x
2
−
8
x
+
a
is divided by
(
3
x
+
3
)
,
it leaves a remainder
24
.
If it is divided by
(
3
x
−
5
)
,
it leaves a remainder
4
4
9
.
Find the value of
a
and
b
(i)
2
,
16
(ii)
0
,
14
(iii)
15
,
2
(iv)
16
,
1
(v)
15
,
1
Question
25
25.
Find the value of
a
and
b
such that
b
x
4
−
x
3
−
25
x
2
+
a
x
is exactly divisible by
(
x
2
+
4
x
−
5
)
(i)
0
,
24
(ii)
25
,
1
(iii)
25
,
2
(iv)
2
,
26
(v)
26
,
1
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (ii)
5) (ii)
6) (v)
7) (iv)
8) (iii)
9) (v)
10) (iii)
11) (ii)
12) (v)
13) (v)
14) (v)
15) (iv)
16) (ii)
17) (v)
18) (iv)
19) (ii)
20) (v)
21) (ii)
22) (iv)
23) (ii)
24) (v)
25) (ii)
