Question

How do you factor `10z^2-17z+3`?

Answer 1

`10z^2-17z+3 = (5z-1)(2z-3)`

Given that the constant term is positive and the middle term is negative, I was looking for a factorization like `(5z-a)(2z-b)` with `a>0`, `b>0` and `ab=3`. That does not give many choices to try.

Of course there might have been a solution of the form `(10z-a)(z-b)`, but the middle term being `-17` - close to `-3xx5` pointed to the first factorization to try.

Answer 2

Factor y = 10x^2 - 17x + 3 = (x -p)(x - q). I use the new AC Method.
Converted trinomial: x^2 - 17x + 3 = (x - p')(x - q')
Compose factor pairs of a.c = 30 -> (1, 30)(2, 15)> This last sum is 17 = -b. Then p' = -2 and q' = -15.
Next: p = p'/2 = -2/10 = -1/5, and q = q'/2 = -15/10 = -3/2
Factored form: y = (x - 1/5)(x - 3/2) = (5x - 1)(2x - 3).