Question 624139
The straightforward approach to finding P(-2) is to replace all the x's with -2's and then simplify. But this process can be tedious: raising -2 to various powers and then do all that adding and /or subtracting.<br>
Synthetic division is a quick, fairly simple way to divide a polynomial by something of the form (x-a). And the Remainder Theorem tells us that for any polynomial, P(x), P(a) will be the remainder of {{{P(x)/(x-a)}}}. These facts combine to explain why we can use synthetic division to find the value of a polynomial. It is often much easier this way to find P(a) than the straightforward approach described above.<br> 
Probably the easiest way to get this wrong is to fail to notice that there is no {{{x^2}}} term. When we set up the synthetic division we must notice this and know to use a 0 for its coefficient:
<pre>
-2 |   1   9    0   -9    2
===       -2  -14   28  -38
      =====================
       1   7  -14   19  -36
</pre>
The remainder of this division is always in the lower right corner. So your remainder, and therefore P(-2), is -36.