Factoring – Signs in Trinomials When we factor trinomials into binomials, it is very important to understand the possible sign combinations. The L in the FOIL pattern for multiplying two binomials stands for “Last”. Example 1 Last × =

The last term of the trinomial is negative. This means that the last terms of the binomials must be opposite is sign. This can be done in two ways. Turn this process around, starting with the trinomial, and determine the signs for the binomial. Example 2

or It doesn’t make any difference at this point which one you write. Adjustments can be made later in the factoring process.

The last term of the trinomial is positive. This means that the last terms of the binomials must be the same sign. Example 3

Since the middle term is negative, use the two negatives.

The last term of the trinomial is positive. This means that the last terms of the binomials must be the same sign. Example 4

Since the middle term is positive, use the two positives.

SUMMARY Trinomial 1.Third term negative Binomials Opposite signs 2.Third term positiveSame signs a)Middle term positive Both signs positive b)Middle term negative Both signs negative

Since the last term of the trinomial is positive, the signs must be the same. Since the middle term is negative, both signs are negative. Example 5

Since the last term of the trinomial is negative, the signs must be opposite. Example 6