Question

Resolve each of the following quadratic trinomials into factors:

6a² + 17ab - 3b²

Answer 1

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)