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## Factoring General Polynomials (grouping number GN)

 WHAT TO DO: HOW TO DO IT: Example: 6t2 + 23t + 20 6t2 + 23t + 20 Multiply 6· 20: GN 6·20 = 120 Find pairs of integer factors (largest first) Sign before last term is + so find pair with the SUM of 23 → 15 + 8 = 23 Both have same sign as middle number + 23 +15, + 8 Rewrite polynomial 6t2 + 23t + 20 with 4 terms having correct signs: 6t2 + 15t + 8t + 20 Group terms 2 by 2 6t2 + 15t + 8t + 20 Factor common term from each group: 3t(2t + 5) + 4(2t + 5) Note that (2 t + 5) is now common factor and factor it out to get: (3t + 4)(2t + 5) Multiply by FOIL to check: Check: Write out answer:   6t 2 + 23t + 20 = (3t + 4)(2t + 5) or (2t + 5)(3t + 4)