Question 1128287
{{{x^3 - kx^2 + 2kx -18}}}

Find the value of {{{k}}} such that {{{x-3}}} is a factor of the above. 

We should attempt synthetic division to find when 
{{{(x^3 - kx^2 + 2kx -18)/(x-3)}}}has a remainder of 0, which would signify that it is a factor of the polynomial.

The synthetic substitution would be set up as:

{{{3}}}| {{{1}}}.....{{{-k}}}.....{{{2k}}}...{{{-18}}}
 
------------------------------------------------------|{{{0}}}

Treating the synthetic division like any other synthetic division problem, we see that

{{{3}}}| {{{1}}}.....{{{-k}}}..........{{{2k}}}.................{{{-18}}}
−----------{{{3}}}........{{{-3k+9}}}.........{{{-3k+27}}}
−−---------{{{1}}}.....{{{-k+3}}}........{{{-k+9}}}.......|{{{0}}}	 
 
If the remainder equals {{{0}}}, then we know that 

{{{-3k+27-18=0}}}

{{{27-18=3k}}}

{{{3k=9}}}

{{{k=3}}}


{{{x^3 - 3x^2 + 2*3x -18}}}

{{{x^3 - 3x^2 + 6x -18}}}

{{{x^3 - 3 x^2 + 6 x - 18 = (x^2 + 6) * (x - 3) + 0}}}