Question 4 - Polynomial Division and Algorithms Practice | Prasnya
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Polynomial Division and Algorithms - Polynomial Division and...
Question 4
00:00
Est. 4 min
Marks:
+4.00
0.00
Passage
Consider the three polynomials:
p
(
x
)
=
4
x
5
+
9
x
4
+
b
1
x
2
+
c
1
p(x) = 4x^5 + 9x^4 + b_1 x^2 + c_1
q
(
x
)
=
−
5
x
4
+
8
x
2
+
b
2
x
+
c
2
q(x) = -5x^4 + 8x^2 + b_2 x + c_2
s
(
x
)
=
x
7
+
72
x
5
+
b
3
x
3
+
c
2
x
2
+
d
3
x
+
c
3
s(x) = x^7 + 72x^5 + b_3 x^3 + c_2 x^2 + d_3 x + c_3
Use this information to answer the given sub-questions.
Question
Which of the following options is/are true?
Comprehension
Hard Difficulty
23 February 2025
A
If
r
1
(
x
)
r_1(x)
is the remainder when
q
(
x
)
q(x)
divides
p
(
x
)
+
q
(
x
)
p(x)+q(x)
, then the maximum possible degree of
r
1
(
x
)
r_1(x)
is 5.
B
If
r
2
(
x
)
r_2(x)
is the remainder when
p
(
x
)
p(x)
divides
s
(
x
)
s(x)
, then the maximum possible degree of
r
2
(
x
)
r_2(x)
is 2.
C
If
t
1
(
x
)
t_1(x)
is the quotient when
q
(
x
)
q(x)
divides
p
(
x
)
p(x)
, then the possible degree of
t
1
(
x
)
t_1(x)
is 1.
D
If
t
2
(
x
)
t_2(x)
is the quotient when
p
(
x
)
p(x)
divides
s
(
x
)
s(x)
, then the possible degree of
t
2
(
x
)
t_2(x)
is 3.