Question 1 - Long division — quotient and remainder; degree of product; end behaviour Practice | Prasnya
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Long division —...
Question 1
00:00
Est. 4 min
Marks:
+5.00
0.00
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2+x)(x+3)
. Let
r
(
x
)
r(x)
and
s
(
x
)
s(x)
be the remainder and the quotient, respectively, obtained when
p
(
x
)
p(x)
is divided by
q
(
x
)
q(x)
. Let
z
(
x
)
=
r
(
x
)
⋅
s
(
x
)
z(x) = r(x) \cdot s(x)
. Which of the following options is/are true?
Multiple correct
Hard Difficulty
13 July 2025
A
z
(
x
)
z(x)
is an even degree polynomial.
B
z
(
x
)
z(x)
is an odd degree polynomial.
C
End behaviour:
z
(
x
)
→
+
∞
z(x) \to +\infty
as
x
→
+
∞
x \to +\infty
.
D
End behaviour:
z
(
x
)
→
+
∞
z(x) \to +\infty
as
x
→
−
∞
x \to -\infty
.
