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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·(Ax 2 ± Bx ± C)
Given a general trinomial: 72x 2 − 60x − 28
Factor out common factor if there is one. 4(18x 2 − 15x − 7)
On Scratch Paper, look at polynomial inside (...): 18x 2 − 15x − 7
Use GN and Clue of Signs 

Multiply first and last coefficients:


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
Check by multiplying out: