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To factor trinomials, start by examining the last sign. If it's positive, the factors must share the same sign (either both positive or both negative). To determine which, check the middle term's sign. If the last sign is positive, the factors are either both positive or both negative; looking at the middle term reveals the correct option. For example, a positive last sign indicates either two positives or two negatives. By referencing the middle term, you can confirm the signs needed for the factors in the trinomial setup.