To factor a trinomial in the form ax^2 + bx + c, find all of the factor pairs that multiply into c, and isolate the pair that also adds up to form b. Substitute the pairs of factors into a pair of binomials that multiply together.
- Identify the factors of c
Consider the problem x^2 - 7x + 12. Find the factors of c (12, in this case) to yield 1, 2, 3, 4, 6 and 12. List these in opposing pairs that multiply to make 12 (1, 12; 2, 6; 3, 4).
- Isolate the correct factors for this problem
Look at each pair of factors to determine which pair adds up to b (-7, in this case). Remember that a negative times a negative yields a positive, which means that both factors end up as negative numbers for the example problem. Write the pairings in this way: 1 + 12 = 13; 2 + 6 = 8; 3 + 4 = 7. Identify -3 and -4 as the factors, as those add up to -7.
- Write the solution in the appropriate format
Break the solution down into a pair of binomials that multiply together. Write the final answer in this way: x^2 - 7x + 12 = (x - 4)(x - 3).