SOLUTION: please explain how to reverse the FOIL method when factoring a polynomial of the form ax^2+bx+c when a=1. Please give an example so that I might understand better.

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Question 165521: please explain how to reverse the FOIL method when factoring a polynomial of the form ax^2+bx+c when a=1. Please give an example so that I might understand better.
Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
start with two binomials, x+j and x+k

FOILing gives __ x^2+kx+jx+kj __ x^2+(k+j)x+kj

the factors of the c term are k and j __ the sum of those factors is the b term

reverse FOILing is finding factors of c that sum to b

EX. __ x^2-5x+6 __ factors of 6 are (±1, ±6) and (±2, ±3)
__ -2 plus -3 is -5
__ x^2-5x+6=(x-2)(x-3)