How do you factor #3m ^ { 3} - 12m ^ { 2} + 27m#?

1 Answer
Jim G.
Sep 7, 2017

#3m(m-2-isqrt5)(m-2+isqrt5)#

Explanation:

#"there is a "color(blue)"common factor"" of " 3m" in all 3 terms"#

#rArr3m(m^2-4m+9)#

#"check the "color(blue)"discriminant " "of "m^2-4m+9#

#"with "a=1,b=-4,c=9#

#Delta=b^2-4ac=16-36=-20#

#"since "Delta<0" there are no real solutions"#

#"we can determine the factors by finding the solutions"#
#"using the "color(blue)"quadratic formula"#

#m=(4+-sqrt(16-36))/2#

#color(white)(m)=(4+-sqrt-20)/2=(4+-2isqrt5)/2#

#rArrm=2+-isqrt5larrcolor(red)" complex solutions"#

#rArr3m^3-12m^2+27m#

#=3m(m-2-isqrt5)(m-2+isqrt5)#

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