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.
-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
The remaining quadratic polynomial is . For finding the other two roots, we can remove the common factor of 2 to get
This factors to give us two rational roots:
The two remaining roots are -1/7 and +1/2.
ANSWER: The three roots, all rational, are -7/2, -1/7, and 1/2.