Exercise 1: Simplifying 7n^3 + 2n^2 + 50 — Possible Solution
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GIVEN
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f(n) = 7n^3 + 2n^2 + 50

STEP 1: IDENTIFYING THE DOMINANT TERM
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Comparing the three terms as n grows large: n^3 grows faster than n^2,
which grows faster than the constant term 50. The dominant (fastest-
growing) term is 7n^3.

STEP 2: DROPPING THE COEFFICIENT AND LOWER-ORDER TERMS
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Per this chapter's own dominant-term rule:
- The 2n^2 term is dropped, since it grows strictly slower than n^3
  and becomes negligible in comparison as n grows.
- The constant 50 is dropped for the same reason - it doesn't grow
  at all.
- The leading coefficient 7 is dropped too, since Big-O only cares
  about growth shape, not the constant multiplier.

RESULT
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f(n) = O(n^3)

WHY THIS WORKS AS AN ANSWER
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Each term is evaluated for whether it could dominate the expression's
growth as n gets large, the dominant term (n^3) is identified
explicitly, and the reasoning for dropping each of the other terms and
the leading coefficient is stated individually rather than just
asserting the final answer.