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Factoring Trinomials by Grouping

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)
 
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