Question 1204305
<br>
(3x-2) is a factor of the polynomial if x=2/3 makes the function value zero.<br>
Since no method was specified, here are three....<br>
(1) Graph the function on a graphing calculator and evaluate the function at x=2/3 and see that the function value is 0.<br>
That's fine...but you don't learn any skills by doing it that way.<br>
(2) With pencil and paper, evaluate the function for x=2/3:<br>
{{{3(2/3)^3-14(2/3)^2+26(2/3)-12}}}
{{{3(8/27)-14(4/9)+26(2/3)-12}}}
{{{24/27-56/9+52/3-12}}}
{{{8/9-56/9+52/3-12}}}
{{{-48/9+52/3-12}}}
{{{-16/3+52/3-12}}}
{{{36/3-12}}}
{{{12-12}}}
{{{0}}}<br>
Good exercise in arithmetic....<br>
(3) Use synthetic division to verify that x=2/3 is a zero of the function.<br><pre>

      |   3 -14  26 -12
  2/3 |       2  -8  12
      +-----------------
          3 -12  18   0</pre>
Synthetic division is a useful skill to have...<br>