Resolve each of the following quadratic trinomials into factors:
Here, coefficient of a2 = 6, coefficient of a = 17b and constant term = - 3b2
We shall now split up the coefficient of middle term i.e., 17b into two parts whose sum is 17b and product is 6 (-3b2) = - 18b2
Clearly,
18b – b = 17b and,
6 (-3b2) = - 36y2
So, we replace middle term 17ab = 18ab – ab
Thus, we have
6a2 +17ab– 3b2 = 6a2 + 18ab - ab – 3b2
= 6a (a + 3b) – b (a + 3b)
= (6a – b) (a + 3b)