Factoring Trinomials

If a trinomial ax+ bx + c will not factor by any other method, use trial and error to fit it into the F O I L pattern:

1. Set up empty parentheses: .

If a,b,c are positive, then both signs are positive .

If b is negative but c is positive, then both signs are negative .

If c is negative, then one sign is positive and the other is negative .

2. Try the factors of a in front positions , and the factors of c in the back positions , until the resulting product is the orginal trinomial.

Example: factor 2x - x - 10

step 1:

step 2:

step 3: The factors of 2 are 2 and 1; the factors of 10 are 10 and 1 or 5 and 2:

(2x + 10)(x - 1) = 2x + 8x - 10

(2x + 5)(x - 2) = 2x+ x - 10

The second trial is almost correct; only the sign of the middle term is wrong. So we change signs:

(2x - 5)(x + 2) = 2x- x - 10

The answer is (2x - 5)(x + 2) .