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How do you factor #18m² n^4-12m² n^3+24m² n²#?

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Jun 7, 2015

#18m^2n^4-12m^2n^3+24m^2n^2#

#=6m^2n^2(3n^2-2n+4)#

#(3n^2-2n+4)# has no simpler linear factors since it's discriminant is negative:

#Delta(3n^2-2n+4) = (-2)^2 - (4xx3xx4)#

#= 4 - 48 = -44#

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