In order to factorize the given expression, we find to find two numbers p and q such that:
p + q = -14, pq = -51
Clearly,
3 – 17 = -14, 3 (-17) = -51
Therefore, split 14a as 3a – 17a
Therefore,
a2 – 14a – 51 = a2 + 3a – 17a – 51
= a (a + 3) – 17 (a + 3)
= (a – 17) (a + 3)