MHB Finding the Largest Root of a Polynomial Using Synthetic Division

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The polynomial \(x^3 - 3x^2 - 6x + 8\) has -2 as the smallest root. Using synthetic division, the polynomial is factored down to \(x^2 - 5x + 4\). This quadratic factors further into \((x - 1)(x - 4) = 0\). The roots of this quadratic are 1 and 4, making 4 the largest root. Therefore, the largest root of the polynomial is 4.
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$\tiny{GRE.al.06}$
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

 
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the largest root is 4
 

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