How to Factor a Simple Trinomial
- 1). Rearrange the trinomial's terms in descending order, placing the squared term first and the constant term last. For example, rewrite the trinomial -12 + x^2 + 4x as x^2 + 4x -- 12.
- 2). List positive and negative factor pairs of the constant, starting with "1." These are numbers that, when multiplied together, produce the constant. In x^2 + 4x -- 12, brainstorm factor pairs of -12. The first few are: 1 and -12, -1 and 12, 2 and -6, -2 and 6. Each time you generate a pair of factors, add them together -- you are trying to find the pair that sum to the coefficient of the middle term. In the example, you want to find two factors of -12 that add up to 4. The desired pair here is -2 and 6, because -2*6 = -12 and -2 + 6 = 4.
- 3). Draw two empty sets of parentheses next to each other, leaving ample space inside each set. In the left-hand portion inside both sets, write the variable from the problem, which in the example is "x." After this, write the pair of factors you found in Step 2, placing one number and its sign inside each set. The solution to the example is (x -- 2)(x + 6).
- 4). Check your answer by multiplying both terms in the first set of parentheses by both terms in the second set of parentheses. The original trinomial should result. This process is sometimes known by the acronym FOIL, which stands for "first, outer, inner, last." In the example, multiply the first terms of each set, x and x, then the outer terms, x and 6, followed by the inner terms, -2 and x, and lastly the last terms, -2 and 6. This produces x^2 + 6x -- 2x -- 12. Combine the two middle terms to obtain x^2 + 4x -- 12, the original trinomial. Hence, (x -- 2)(x + 6) is the correct factorization.
