How do you completely factor x^3-x^2-14x+25 given x-3 is one of the factors?

Nov 2, 2016

$x - 3$ is not a factor.

Explanation:

Factor ${x}^{3} - {x}^{2} - 14 x + 25$ given $x - 3$ is a factor.

$3 | 1 \textcolor{w h i t e}{a a} - 1 \textcolor{w h i t e}{a a} - 14 \textcolor{w h i t e}{a a a} 25$
$\textcolor{w h i t e}{a a} \downarrow \textcolor{w h i t e}{a a a a} 3 \textcolor{w h i t e}{a a a a a} 6 \textcolor{w h i t e}{a} - 24$
$\textcolor{w h i t e}{a a a}$--------------------------------
$\textcolor{w h i t e}{a a a} 1 \textcolor{w h i t e}{{a}^{22} a a} 2 \textcolor{w h i t e}{{a}^{2} a} - 8 \textcolor{w h i t e}{a a a} 1$

The remainder is 1 instead of zero, so $x - 3$ is not a factor.

Perhaps the $25$ was a typo, and should have been a $24$.