Question 5 - End behaviour — determined by degree and sign of leading coefficient Practice | Prasnya
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Week 4
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Graphs of Polynomials — Intercepts, Multiplicities, and End Behaviour - Graphs of Polynomials...
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End behaviour —...
Question 5
00:00
Est. 3 min
Marks:
+4.00
0.00
Passage
Consider a polynomial
p
(
x
)
=
(
x
2
−
1
)
(
x
3
−
4
x
2
+
4
x
)
(
x
3
−
10
x
2
+
33
x
−
36
)
p(x)=(x^2-1)(x^3-4x^2+4x)(x^3-10x^2+33x-36)
such that
t
(
x
)
=
(
x
3
−
6
x
2
+
9
x
)
t(x)=(x^3-6x^2+9x)
divides
p
(
x
)
p(x)
.
s
(
x
)
=
(
x
2
−
5
x
+
4
)
s(x)=(x^2-5x+4)
divides
p
(
x
)
p(x)
.
q
(
x
)
q(x)
is the quotient when
p
(
x
)
p(x)
is divided by the polynomial
z
(
x
)
=
(
x
+
1
)
t
(
x
)
s
(
x
)
z(x)=(x+1)t(x)s(x)
. Use this information to answer the given subquestions:
Question
Which of the following options is/are true?
Comprehension
Medium Difficulty
16 July 2023
A
The minimum value of the quotient
q
(
x
)
q(x)
is
0
0
.
B
p
(
x
)
p(x)
is an odd degree polynomial.
C
End behavior
p
(
x
)
→
+
∞
p(x)\to +\infty
as
x
→
+
∞
x\to +\infty
.
D
End behavior
p
(
x
)
→
+
∞
p(x)\to +\infty
as
x
→
−
∞
x\to -\infty
.