Finding the Largest Root of a Polynomial Using Synthetic Division

[karush]

$\tiny{GRE.al.06}$
For the polynomial $x^3-3x^2-6x+8\quad -2$ is the smallest root.
Find the largest root.
$a.\, -1 \quad b.\, 1 \quad c.\, 2 \quad d.\, 3 \quad e.\, 4$
Since -2 is a root then use synthetic division

$\begin{array}{r|rrrr}
-2&1&-3&-6&8\\
& & -2& 10&-8\\
\hline
&1& -5& 4&0
\end{array}$
then
$x^{2}- 5 x+4=(x-1)(x-4)=0$
so the largest factor is 4

hopefully
I doubt if it could done without some calculation maybe

 

[skeeter]

the largest root is 4