1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n) = 5n+20 n³ - 10 n² + 10

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1. Prove the following polynomial is e(n). Use algebraic manipulations.
P(n)=5n+20 n³ - 10 n² + 10
(a) Prove 0(n*).
(b) Prove (n*).
Therefore,
4
3
P(n) = 5n²+ 20n - 10 m² +10
2
<5n4
+201³
+10
2
4
3
P(n) = 5n²+ 20 m²
3
<5n4 +201³ (^_) + 10 (212) 4
101)
< n²4 (5+02 + 0.000000,
<m² (52001)
>n4 (5-0.1)
4
> 4.9 n
of 6
4.9 n
M2lcv
1
OD
2
> 5n²4-10 n²
2
2 n
Σ 5n²-101² (70)² 7210, (+)2)
>
10
10 m² +10
m310
< P(n) < 5.2001 n'
Discard Neg Terms
m2100, (n))
Note this
transformatio
may be applied
only to pas
Discord Pos Terus
This
man
be applied)
to only Nag terms,
m> 100
Transcribed Image Text:ud + 1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n)=5n+20 n³ - 10 n² + 10 (a) Prove 0(n*). (b) Prove (n*). Therefore, 4 3 P(n) = 5n²+ 20n - 10 m² +10 2 <5n4 +201³ +10 2 4 3 P(n) = 5n²+ 20 m² 3 <5n4 +201³ (^_) + 10 (212) 4 101) < n²4 (5+02 + 0.000000, <m² (52001) >n4 (5-0.1) 4 > 4.9 n of 6 4.9 n M2lcv 1 OD 2 > 5n²4-10 n² 2 2 n Σ 5n²-101² (70)² 7210, (+)2) > 10 10 m² +10 m310 < P(n) < 5.2001 n' Discard Neg Terms m2100, (n)) Note this transformatio may be applied only to pas Discord Pos Terus This man be applied) to only Nag terms, m> 100
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