Trinomial Factoring
Trinomial Factoring
A trinomial, if factorable, will factor into the product of two binomials. Since there is no common factor to extract and the coefficient of the first term is one, we can proceed with a simple process for factoring.
In effect, we are undoing the process of "FOIL"ing. For example,
(x + 2) (x - 1) = x^{2} - x + 2x - 2 = x^{2} + x - 2
So, you see the first term of the trinomial factors into the first binomial terms:
(x ) (x )
Now what about the last terms of the binomial? We look to the last term of the trinomial (-2). What two factors multiply to give -2, but sum to give the middle term? Well, the only two factors of for negative two are either (-1)(2) or (1)(-2). But which pair sums to give the middle term of +1? (-1)(2)
(x - 1) (x + 2)
For your problem, we do the same.
x^{2} + 4x + 4
Simply write out empty parentheses to start. Since the coefficient of the first term is 1, we can factor the first term into
(x ) (x )
Now, factors of 4 that could also sum the middle term, which is also 4. The sign on each factor must be positive to sum to the middle term.
1 4
+2 +2
(x + 2) (x + 2) ==> You can always FOIL this out to make sure the factorization is correct!