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altavistard
Perhaps you meant   (a^3+14a^2+33a-20)   /   (a+4), for division by (a+4).  

Do you know synthetic division?  If so, that'd be a great way to accomplish this division.  Assume that (a+4) is a factor of a^3+14a^2+33a-20; then assume that -4 is the corresponding root of a^3+14a^2+33a-20.

Perform synth. div.  If there is no remainder, then you'll know that (a+4) is a factor and will also have the quoitient.

-4  /   1   14   33   -20
     ___    -4_-40    28___________
          1   10   -7       8

Here the remainder is not zero; it's 8.  However, we now know that the quotient is 1a^2 + 10a - 7 with a remainder of 8.

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