Trinomials Requiring Decomposition You must have already taken out a common factor. Example #1: 6x2 + 19x + 10 Find numbers that: - multiply to +60 (product of first and last coefficient) - add to +19 (middle coefficient): They are +15 and +4 ... use them to split the middle term: = 6x2 + 15x + 4x + 10 (order of the no's doesn't matter) Now find common factors for each group of two: = 3x (2x + 5) + 2 (2x + 5) The common bracket is the common factor: = (2x + 5) (3x + 2) Example #2: 8x2 - 2xy - 3y2 Find numbers that multiply to -24 (product of 8 and -3) and add to -2 : They are +4 and -6 When negatives are involved, double check that the numbers do both things. Then use them to split the middle term: = 8x2 + 4xy - 6xy - 3y2 Now find common factors for each group of two: = 4x (2x + y) - 3y (2x + y) The common bracket is the common factor: = (2x + y) (4x - 3y) You should have the times tables up to 12 x 12 memorized by now. If not, make that a priority. Many of these questions will be unnecessarily difficult if you don't have the times tables memorized. Return to 'Explanations' Page | Back to Flow Chart