title: How are the following functions O(N^3)?
body: <p>I'm taking the "Intro To Algorithms" course on Coursera, and I've arrived at the video which deals with Big-Theta, Big-Omega and Big-O notation.  The end-of-video quiz presents the following question:</p>
  
  <pre><code>Q: Which of the following functions is O(N^3)?
  
  a) 11N + 15lgN + 100
  b) (N^2)/3
  c) 25,000*(N^3)
  d) All of the above
  </code></pre>
  
  <p>I answered "c" and was told my answer was incorrect, and that the correct answer is actually "d".  The explanation provided by the course wasn't much help:</p>
  
  <pre><code>Recall that big-Oh notation provides only an upper bound on the growth
  rate of a function as N gets large. In this course, we primarily use 
  tilde notation because it more accurately describes the function—it 
  provides both an upper and lower bound on the function as well as the 
  coefficient of the leading term.
  </code></pre>
  
  <p>I was under the impression that one should drop the lesser-order terms (i.e. "15lgN + 100") and focus only on the highest-order terms.  Furthermore, I can't see how N^3 could be the upper bound on a quadratic (as opposed to a cubic) function like N^2.</p>
  
  <p>So my question is, why are "a" and "b" classified as O(N^3) in this case?</p>