Question 2 - Graphs of Polynomials — Intercepts, Multiplicities, and End Behaviour Practice | Prasnya
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Graphs of Polynomials — Intercepts, Multiplicities, and End Behaviour - Graphs of Polynomials...
Question 2
00:00
Est. 2 min
Marks:
+4.00
0.00
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x) = -x^5 + 5x^4 - 7x - 2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x) = -x^5 + 5x^4 - x^2 - 2
. Which of the following options is/are true?
Multiple correct
Medium Difficulty
26 October 2025
A
q
(
x
)
→
−
∞
q(x) \to -\infty
as
x
→
∞
x \to \infty
.
B
p
(
x
)
→
∞
p(x) \to \infty
as
x
→
∞
x \to \infty
.
C
p
(
x
)
p(x)
has at most 5 turning points.
D
The quotient obtained while dividing
q
(
x
)
q(x)
by
p
(
x
)
p(x)
is a constant.
