SOLUTION: Show that x-c is not a factor of f(x)={{{3x^4+x^2+5}}} for any real number c.

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Question 204627: Show that x-c is not a factor of f(x)= for any real number c.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Let's divide: 

 by  using synthetic division:

We must express  as 

 c | 3       0       1        0        5 
   |        3c      3c2     c+3c3   c2+3c4
    ----------------------------------------
     3      3c    1+3c2     c+3c3  5+c2+3c4 

The remainder is 5+c2+3c4.  This is always
a positive number because even powers of a
real number are never negative. Thus this
remainder can never be 0.

Edwin
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