Question 143720
Someone, PLEASE HELP, this is a problem i have never seen before. i would appeciate any help just to get started. 
Evaluate {{{P(-1/2)}}} if {{{P(x) = 2x^4 + x^3 + 12}}}
<pre>
There are two methods to find {{{P(-1/2)}}}

First method:  by straight-forward plugging in {{{-1/2}}} for x

{{{P(x) = 2x^4 + x^3 + 12}}}

{{{P(1/2) = 2(-1/2)^4 + (-1/2)^3 + 12}}}

{{{P(1/2) = 2(1/16) + (-1/8) + 12}}}

{{{P(1/2) = 1/8 - 1/8 + 12}}}

{{{P(1/2) = 12}}}


Second method:  by synthetic division and the remainder
theorem which says that you get the same answer when you

1. plug a number directly into a polynomial 

as you get when you

2. write that number to the left of a synthetic division,
do the synthetic division, and take only the remainder,
which is the rightmost number on the bottom line of the
synthetic division. 

Notice that since the {{{x^2}}} and {{{x}}} terms are 
missing in the original polynomial, we have to insert
0's for them as placeholders:

{{{-1/2}}} | 2    1    0    0   12
     |     -1    0    0    0
      ----------------------
       2    0    0    0   12

The last number on the right {{{12}}} is the remainder
which by the remainder theorem is {{{P(1/2)}}}


Edwin</pre>