Factoring Completely General Quadratic Trinomials

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WHAT TO DO:	HOW TO DO IT:
Given a trinomial of type ax² ± bx ± c that has at least one common factor. Factor out all of the common factors then look at the remaining quadratic trinomial.	k·(Ax² ± Bx ± C)
Given a general trinomial:	72x² − 60x − 28
Factor out common factor if there is one.	4(18x² − 15x − 7)
On Scratch Paper, look at polynomial inside (...):	18x² − 15x − 7
Use GN and Clue of Signs Multiply first and last coefficients:	GN 18·7 = 126
NOTE: Last sign is − therefore Find all pairs of factors of 126 with difference of 15.
The largest factor of the pair gets sign of middle term, − the other is positive:	− 21 and + 6
Rearrange polynomial using these values as coefficients of x	18x² − 21x + 6x − 7
Factor common factor from each group:	3x(6x − 7) + 1(6x −7)
Combine with first term factored out the complete factors of: 72x² - 60x - 28	4(3x + 1)(6x − 7) answer
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