synthetic division

Question

Find f (c) either by using synthetic division and the remainder theorem or by evaluating f (c) directly.

f (x) = 7x^4 - 7x^3 - 6x^2 - 8x - 3 and c = 6

Answer 1

I will use synthetic division.  If the remainder is zero, the f(c)=0.  Otherwise, the remainder is the value of f(c).

 

6 | 7       -7           -6                 -8                  -3

 

              42        -210            -1296           -7824

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     7      -35       -216             -1304           -7827

 

 

f(6) = -7827