Question 194080
If P(x) = 3x^5 - 8x^4 + 3x^3 + 2x^2 - 16x + 14, then P(3) = ?
...is it 682?
<pre><font size = 4 color = "indigo"><b>
No it isn't.

There are two ways to find P(3).

Method 1.  Substitute 3 for x in

{{{P(x) = 3x^5 - 8x^4 + 3x^3 + 2x^2 - 16x + 14}}}

{{{P(3) = 3(3)^5 - 8(3)^4 + 3(3)^3 + 2(3)^2 - 16(3) + 14}}}

{{{P(3) = 3(243) - 8(81) + 3(27) + 2(9) - 48 + 14}}}

{{{P(3) = 729 - 648 + 81 + 18 - 48 + 14}}}

{{{P(3) = 146}}}

Method 2 (Much easier, by synthetic division).

Start with this:

3 | 3 -8  3   2 -16   14
  |     
   ---------------------
   
and end up with this:

3 | 3 -8  3   2 -16   14
  |    9  3  18  60  132 
   ---------------------
    3  1  6  20  44  146

The answer, 146, is in the lower right 
corner of the synthetic division.

Edwin</pre>