factor by grouping number method using FOIL
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We want to construct an expression that when simplified gives 2x^2 + 5x - 3, that look like (ax+b)(cx+d), and we need to find what a, b, c and d are.
By FOIL, the first terms product F: is a*c*x^2
the second term product O: is a*d*x
the third term product I: is b*c*x
and the last product is L: b*d.
We need to match that with 2*x^2 + 5x - 3, which means that:
a*c = 2 [x^2 terms]
a*d + b*c = 5 [x terms]
b*d = -3 [constant terms]
We get that b=-1, d = 3, a = 2, c =1 or
Just to confirm: 2x*x +6*x -1*x -3 = 2x^2 + 5x - 3, as desired.
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