Find the factored form of 4x2– x - 14.

(4x + 7)(x - 2)

Step-by-step 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)

-50/3 is the final answer! : )