Answer:
(4x + 7)(x - 2)
Explanation:
Synthetic division can be a very useful tool in factoring, although there are certainly other methods.
-14 is the constant term; its factors here MAY include ±2 and/or ± 7.
Let's use synthetic division to determine whether or not 2 is a root of the quadratic:
2 / 4 -1 -14
8 14
--------------------
4 7 0
Because the remainder here is zero (0), we have verified that 2 is a root and (x - 2) is a factor of 4x^2 - x - 14. Note that the remaining coefficients, 4 and 7, indicate that the other factor is 4x + 7.
Thus, 4x^2– x - 14 = (4x + 7)(x - 2)