Consider the Statement $3 \left| x ^ { 2 } \right| \leq \left| 3 x ^ { 2 } + 17 x + 5 \right| \leq 25 \left| x ^ { 2 } \right| \quad \text { for all } x > 1 \text {. }$

question 18

Essay

Consider the statement: $3 \left| x ^ { 2 } \right| \leq \left| 3 x ^ { 2 } + 17 x + 5 \right| \leq 25 \left| x ^ { 2 } \right| \quad \text { for all } x > 1 \text {. }$
Express this statement using $\Theta \text {-notation. }$

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Definitions:

Unenforceable

Pertaining to a contract or clause that is not legally binding and cannot be upheld by a court of law due to certain legal deficiencies.

Bank Robbery

The illegal act of stealing money or assets from a bank while it is open for business.

Implied-In-Fact Contract

A contract implied by direct or indirect acts of the parties.

Unfairly Benefited

A situation where one party gains an advantage or profit at the expense of another in an unjust manner.