Question 1190367


given that{{{x-3}}} is a factor of

{{{x^3-5x^2-14x+6}}}

use long division to see if it could be factored completely

if we got reminder, than it's not possible to factor completely


---------------({{{x^2-2x-20}}}
{{{(x-3)}}}|{{{x^3-5x^2-14x+6}}}
---------------{{{x^3-3x^2}}}.....subtract
-------------------{{{-2x^2}}}.....bring {{{-14x}}} down
-------------------{{{-2x^2-14x}}}
-------------------{{{-2x^2+6x}}}....subtract
----------------------------{{{-20x}}}....bring {{{6}}} down
-----------------------------{{{-20x+6}}} 
-----------------------------{{{-20x+60}}}....subtract
-------------------------------------{{{-54}}}->reminder

so,

{{{x^3 - 5 x^2 - 14 x + 6 = (x^2 - 2 x - 20)(x - 3) + (-54)}}}