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Byju's Answer
Standard X
Mathematics
Cubic Polynomial
Which of the ...
Question
Which of the following is a cubic polynomial ?
A
x
3
+
3
x
2
−
4
x
+
3
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B
x
2
+
4
x
−
7
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C
3
x
2
+
4
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D
3
(
x
2
+
x
+
1
)
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Solution
The correct option is
C
x
3
+
3
x
2
−
4
x
+
3
A cubic polynomial is a polynomial of degree
3
, or in simpler words highest power of
x
is
3
.
It is of the form
f
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
where
a
,
b
,
c
,
d
belongs to real numbers.
We can see that in option A,
x
has the highest power
3
and
a
=
1
,
b
=
3
,
c
=
−
4
and
d
=
3
.
Rest of the options
B
,
C
,
D
have the highest power as
2
.
Hence, they are quadratic polynomials.
Correct option is
A
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Similar questions
Q.
Find the remainder polynomial when the cubic polynomial
x
3
−
3
x
2
+
4
x
+
5
is divided by
x
−
2
.
Q.
If
f
(
x
)
+
2
f
(
1
−
x
)
=
x
2
+
1
∀
x
ϵ
R
then f(x) is
Q.
(
7
−
4
√
3
)
x
2
−
4
x
+
3
+
(
7
+
4
√
3
)
x
2
−
4
x
+
3
=
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Q.
The polynomial which when divided by −x
2
+ x − 1 gives a quotient x − 2 and remainder 3, is
(a) x
3
− 3x
2
+ 3x − 5
(b) −x
3
− 3x
2
− 3x − 5
(c) −x
3
+ 3x
2
− 3x + 5
(d) x
3
− 3x
2
− 3x + 5