# 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)?

Oct 16, 2015

See the explanation section, below.

#### Explanation:

Here is the division $f \frac{x}{x - 6}$ 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 $f \left(6\right)$

So $f \left(6\right) = 8 , 798$