algebra
posted by sam on .
Megan factored the expression (12x^2+52x35) as (2x+5)(6x7) but when Jacob applied FOIL principle and multiplied out (2x+5)(6x7) he got (12x^2+44x35),thus megan's solution does not appear to check please help megan to understand better.Explain your reasoning and correctly factor the original expression if possible If the expression is a prime please state so

First of all I changed it into
 (12x^2  52x + 35)
After 4 tries I had
 (2x7)(6x5) or (72x)(6x5) or (2x7)(56x)
(I use a method where I list the factors of the first and last numbers, and then take sum or differences of crossproducts
e.g.
3 2 1 ....... 5 7
4 6 12 ...... 7 5
2x5 + 6x7 = 52, my middle term
This is the fastest way to factor trinomials, too bad nobody seems to teach this method any more. 
I came up with (6x5)(2x7)

yes,
that was my first answer I gave you.
surely you realize that
(6x5)(2x7) =  (2x7)(6x5)