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Factoring General Polynomials (Grouping Number GN)

WHAT TO DO: HOW TO DO IT:
Example: 6x2 + 23x + 20 6x2 + 23x + 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 6x2 + 23x + 20 with 4 terms having correct signs: 6x2 + 15x + 8x + 20
Group terms 2 by 2 6x2 + 15x + 8x + 20
Factor common term from each group: 3x(2x + 5) + 4(2x + 5)
Note that (2x + 5) is now common factor and factor it out to get: (3x + 4)(2x + 5)
Multiply by FOIL to check:

Check:

Always Check:

 
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