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)


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