Expert: Steve Holleran - 2/16/2008

Question
Use synthetic division to find each function value.
g(x) = x^6 -4x^4 + 3x^2 + 2
A)g(2)
B)g(-4)
C)g(3)
D)g(-1)


Answer
Hi Kristin,

Okay, these all go the same way, so I'll show g(2), and you can verify the others, because its exactly the same procedure:

When you use synthetic division, be sure to pick off the coefficients of the terms along with their signs, and also to enter "0" for any missing powers.  Since this polynomial has no fifth, third or first degree terms, the set up would be :

   2 |  1    0    -4    0    3    0    2
     |
     |------------------------------------

To start, bring down the first coefficient, the 1, and then multiply by the two and enter the result in the next column.  Add that column, then continue to multiply and add.  The final entry on the bottom is the value of g(2):

   2 |  1    0    -4    0    3    0    2
     |
     |       2     4    0    0    6    12
      -----------------------------------

        1    2    0    0    3    6    |  14

So, g(2) = 14

Similarly, I get g(-4) = 3122

                g(3) = 1244

                g(-1) = 2

I hope you can follow ok.

Steve