Question 1138498
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(1) Substitute x=1 to see if x=1 is a root:<br>
{{{2+3-12+7 = 0}}}<br>
Yes, x=1 is a root.  Use synthetic division to divide out the factor x-1.<br><pre>

 1  |  2  3  -12  7
    |     2    5 -7
    +--------------
       2  5   -7  0<br></pre>
The remainder is 0, so x=1 is a root; (x-1) is a factor.<br>
{{{2x^3+3x^2-12x+7 = (x-1)(2x^2+5x-7)}}}<br>
(2) Factor the remaining quadratic by whatever method you know.<br>
{{{2x^3+3x^2-12x+7 = (x-1)(2x+7)(x-1)}}}<br>