+23254 If you do it by trial-and-error, there are a lot of possibilities;
15 can be factored as (1 and 15) or (3 and 5)
32 can be factored as (1 and 32) or (2 and 16) or (4 and 8) or (8 and 4) or (16 and 2) or (32 and 1)
Since the last term is positive, the two factors must either be both positive or both negative; since the middle term is negative, they must both be negative.
(n - 1)(15n - 32) =
(n - 2)(15n - 16) =
(n - 4)(15n - 8) =
(n - 8)(15n - 4) =
(n - 16)(15n - 2) =
(n - 32)(15n - 1) =
(3n - 1)(5n - 32) =
(3n - 2)(5n - 16) =
(3n - 4)(5n - 8) =
(3n - 8)(5n - 4) =
(3n - 16)(5n - 2) =
(3n - 32)(5n - 1) =
One of the above is correct, the problem is to determine which of the above has the correct middle term, the O and I of FOIL.
It's there ...
+23254 If you do it by trial-and-error, there are a lot of possibilities;
15 can be factored as (1 and 15) or (3 and 5)
32 can be factored as (1 and 32) or (2 and 16) or (4 and 8) or (8 and 4) or (16 and 2) or (32 and 1)
Since the last term is positive, the two factors must either be both positive or both negative; since the middle term is negative, they must both be negative.
(n - 1)(15n - 32) =
(n - 2)(15n - 16) =
(n - 4)(15n - 8) =
(n - 8)(15n - 4) =
(n - 16)(15n - 2) =
(n - 32)(15n - 1) =
(3n - 1)(5n - 32) =
(3n - 2)(5n - 16) =
(3n - 4)(5n - 8) =
(3n - 8)(5n - 4) =
(3n - 16)(5n - 2) =
(3n - 32)(5n - 1) =
One of the above is correct, the problem is to determine which of the above has the correct middle term, the O and I of FOIL.
It's there ...
