2x^2+5x-3= using FOIL

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factor by grouping number method using FOIL

Aug 23rd, 2015

Hi there! Thank you for the opportunity to help you with your question!

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

(2x-1)(x+3).


Just to confirm: 2x*x +6*x -1*x -3 = 2x^2 + 5x - 3, as desired.

Please let me know if you need any clarification. Always glad to help!
Aug 23rd, 2015

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