Question 1208854
<br>
You are given a cubic equation and one of its roots.  Use synthetic division (or long division) to reduce the cubic equation to a quadratic equation; then use factoring or the quadratic formula to find the two remaining roots.<br><pre>

  -3.5  |  28   88  -37   -7
        |
        +--------------------
           28

  -3.5  |  28   88  -37   -7
        |      -98
        +--------------------
           28  -10

  -3.5  |  28   88  -37   -7
        |      -98   35
        +--------------------
           28  -10   -2

  -3.5  |  28   88  -37   -7
        |      -98   35    7
        +--------------------
           28  -10   -2    0</pre>
The remaining quadratic polynomial is {{{28x^2-10x-2}}}.  For finding the other two roots, we can remove the common factor of 2 to get {{{14x^2-5x-1}}}<br>
This factors to give us two rational roots:<br>
{{{14x^2-5x-1=(7x+1)(2x-1)}}}<br>
The two remaining roots are -1/7 and +1/2.<br>
ANSWER: The three roots, all rational, are -7/2, -1/7, and 1/2.<br>