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Mathematics
Problem
Consider the two polynomials
p
(
x
)
=
4
x
6
−
3
x
2
+
1
p(x)=4x^{6}-3x^{2}+1
p
(
x
)
=
4
x
6
−
3
x
2
+
1
and
q
(
x
)
=
−
5
x
7
+
x
3
−
2
q(x)=-5x^{7}+x^{3}-2
q
(
x
)
=
−
5
x
7
+
x
3
−
2
. Which of the two grows faster in magnitude as
x
→
∞
x\to\infty
x
→
∞
? State the feature of each polynomial that justifies your answer.
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