EduSahara™ Assignment
Name : Polynomial Division
Chapter : Polynomials
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
If (x - a) is a factor of f(x), then f(a) = 0
b)
A linear polynomial in one variable has only one root
c)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
d)
A polynomial of degree n has atmost n zeros
e)
Zero of a polynomial and root of the polynomial are synonymous
f)
Zero of a polynomial and zero polynomial are synonymous
g)
If (x + a) is a factor of f(x), then f(a) = 0
(i)
{f,d,e}
(ii)
{f,a}
(iii)
{a,b,c,d,e}
(iv)
{g,b}
(v)
{f,g,c}
Question
2
2.
Which of the following are true ?
a)
If the degree of p(x) is less then the degree of d(x), we should not divide p(x) with d(x)
b)
If p(x) is divided by (x - a), the remainder is p(a)
c)
If p(a) = 0, then (x + a) perfectly divides p(x)
d)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
(i)
{c,a}
(ii)
{a,b}
(iii)
{c,b,a}
(iv)
{d,b}
(v)
{c,d,a}
Question
3
3.
The quotient when
2
p
is divided by
1
is
(i)
2
p
(ii)
5
p
(iii)
3
p
(iv)
p
(v)
0
Question
4
4.
The quotient when
(
−
5
u
2
)
is divided by
(
u
+
8
)
is
(i)
(
−
3
u
+
40
)
(ii)
(
−
7
u
+
40
)
(iii)
(
−
6
u
+
40
)
(iv)
(
−
5
u
+
40
)
(v)
(
−
4
u
+
40
)
Question
5
5.
The quotient when
(
−
6
r
+
1
)
is divided by
(
r
−
5
)
is
(i)
(
−
6
)
(ii)
(
−
7
)
(iii)
(
−
4
)
(iv)
(
−
5
)
(v)
(
−
9
)
Question
6
6.
The quotient when
(
−
7
i
2
−
6
i
+
9
)
is divided by
(
i
−
1
)
is
(i)
(
−
7
i
−
13
)
(ii)
(
−
6
i
−
13
)
(iii)
(
−
5
i
−
13
)
(iv)
(
−
8
i
−
13
)
(v)
(
−
10
i
−
13
)
Question
7
7.
The quotient when
(
−
9
m
2
+
8
m
)
is divided by
(
m
−
3
)
is
(i)
(
−
7
m
−
19
)
(ii)
(
−
9
m
−
19
)
(iii)
(
−
11
m
−
19
)
(iv)
(
−
8
m
−
19
)
(v)
(
−
10
m
−
19
)
Question
8
8.
The quotient when
(
−
3
z
3
−
5
z
−
4
)
is divided by
(
z
2
−
8
z
−
9
)
is
(i)
(
−
3
z
−
24
)
(ii)
(
−
z
−
24
)
(iii)
(
−
4
z
−
24
)
(iv)
(
−
2
z
−
24
)
(v)
(
−
5
z
−
24
)
Question
9
9.
The quotient when
(
7
a
4
−
3
a
3
+
2
a
2
−
3
a
−
2
)
is divided by
(
a
2
+
16
a
+
64
)
is
(i)
(
10
a
2
−
115
a
+
1394
)
(ii)
(
5
a
2
−
115
a
+
1394
)
(iii)
(
6
a
2
−
115
a
+
1394
)
(iv)
(
7
a
2
−
115
a
+
1394
)
(v)
(
8
a
2
−
115
a
+
1394
)
Question
10
10.
The remainder when
(
−
4
a
2
)
is divided by
(
a
−
5
)
is
(i)
(
−
102
)
(ii)
(
−
100
)
(iii)
(
−
99
)
(iv)
(
−
97
)
(v)
(
−
101
)
Question
11
11.
The remainder when
(
4
e
−
8
)
is divided by
(
e
+
1
)
is
(i)
(
−
9
)
(ii)
(
−
15
)
(iii)
(
−
13
)
(iv)
(
−
12
)
(v)
(
−
11
)
Question
12
12.
The remainder when
(
4
g
2
+
g
)
is divided by
(
g
+
1
)
is
(i)
4
(ii)
6
(iii)
3
(iv)
1
(v)
2
Question
13
13.
The remainder when
(
−
2
b
2
−
7
b
+
4
)
is divided by
(
b
−
7
)
is
(i)
(
−
144
)
(ii)
(
−
140
)
(iii)
(
−
145
)
(iv)
(
−
142
)
(v)
(
−
143
)
Question
14
14.
The remainder when
(
3
j
3
−
9
j
2
+
5
)
is divided by
(
j
+
5
)
is
(i)
(
−
598
)
(ii)
(
−
596
)
(iii)
(
−
595
)
(iv)
(
−
593
)
(v)
(
−
594
)
Question
15
15.
The remainder when
(
2
r
4
+
9
r
3
−
3
r
2
+
6
r
+
6
)
is divided by
(
r
2
+
8
r
+
12
)
is
(i)
(
−
143
r
−
342
)
(ii)
(
−
141
r
−
342
)
(iii)
(
−
144
r
−
342
)
(iv)
(
−
140
r
−
342
)
(v)
(
−
142
r
−
342
)
Question
16
16.
The remainder when
(
6
j
4
+
j
3
−
3
j
+
6
)
is divided by
(
j
2
−
16
j
+
63
)
is
(i)
(
12672
j
−
73956
)
(ii)
(
12671
j
−
73956
)
(iii)
(
12670
j
−
73956
)
(iv)
(
12667
j
−
73956
)
(v)
(
12669
j
−
73956
)
Question
17
17.
(
6
x
3
+
x
2
−
5
x
−
2
)
÷
(
−
2
x
2
+
x
+
1
)
=
(i)
(
−
4
x
−
2
)
(ii)
(
−
2
x
−
2
)
(iii)
(
−
3
x
+
2
)
(iv)
(
−
3
x
−
2
)
(v)
(
3
x
−
2
)
Question
18
18.
(
4
x
4
−
24
x
3
+
32
x
2
+
24
x
−
36
)
÷
(
2
x
3
−
10
x
2
+
6
x
+
18
)
=
(i)
(
3
x
−
2
)
(ii)
(
x
−
2
)
(iii)
(
2
x
+
2
)
(iv)
(
−
2
x
−
2
)
(v)
(
2
x
−
2
)
Question
19
19.
(
−
3
x
5
+
4
x
4
+
13
x
3
−
6
x
2
−
20
x
−
8
)
divided by
(
−
3
x
3
+
x
2
+
8
x
+
4
)
=
(i)
(
x
2
−
x
−
2
)
(ii)
(
x
2
+
x
−
2
)
(iii)
(
x
2
−
2
x
−
2
)
(iv)
(
x
2
−
x
+
2
)
(v)
(
x
2
−
2
)
Question
20
20.
(
x
3
+
4
x
2
)
÷
x
(i)
(
x
2
+
5
x
)
(ii)
(
x
2
+
4
x
)
(iii)
4
x
(iv)
(
−
x
2
+
4
x
)
(v)
(
x
2
−
4
x
)
Question
21
21.
(
2
x
4
+
11
x
3
+
15
x
2
)
÷
(
2
x
2
+
5
x
)
(i)
(
x
2
+
4
x
)
(ii)
(
x
2
+
3
x
)
(iii)
3
x
(iv)
(
x
2
−
3
x
)
(v)
(
−
x
2
+
3
x
)
Question
22
22.
(
8
x
4
−
46
x
3
−
214
x
2
−
180
x
)
÷
(
2
x
2
−
14
x
−
36
)
(i)
(
4
x
2
+
5
x
)
(ii)
(
4
x
2
+
4
x
)
(iii)
(
4
x
2
−
5
x
)
(iv)
(
4
x
2
+
6
x
)
(v)
(
−
4
x
2
+
5
x
)
Assignment Key
1) (iii)
2) (ii)
3) (i)
4) (iv)
5) (i)
6) (i)
7) (ii)
8) (i)
9) (iv)
10) (ii)
11) (iv)
12) (iii)
13) (v)
14) (iii)
15) (v)
16) (iii)
17) (iv)
18) (v)
19) (i)
20) (ii)
21) (ii)
22) (i)
