Question

How do you use synthetic division and the remainder theorem to find the indicated function value `f(x)=x^4+4x^3+5x^2-3x-4`; f(6)?

Answer 1

See the explanation section, below.

Explanation:

Here is the division `f(x)/(x-6)` using synthetic division:

#{: (6,"|",1,4,5,-3,-4), ( " ",|," ",36,240,1470,8802), (" "," --","--","---","----", "-----","-------"), (" "," ",6,40,245,1467,8798) :}#

The remainder is `8,798` and it is also `f(6)`

So `f(6) = 8,798`