Trinomial Factoring

Trinomial Factoring

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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?

(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!**

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