How do you factor #15x^4-39x^3+18x^2#?

1 Answer
Jul 25, 2017

Answer:

#=3x^2(x-2)(5x-3)#

Explanation:

Take out a common factor of #3x^2# first:

#15x^4 -39x^3 +18x^2#

#=3x^2(5x^2 -13x+6)#

Find factors of #5 and 6# whose products ADD to #13#

#" "5" and "6#
#" "darrcolor(white)(xxxx)darr#

#" "1 color(white)(xxxxx)2" "rarr 5 xx 2 = 10#
#" "5color(white)(xxxxx)3" "rarr 1xx3 = ul3#
#color(white)(xxxxxxxxxxxxxxxxxxx)13#

These are the correct factors: the signs in both brackets will be #-#

#=3x^2(5x^2 -13x+6)#

#=3x^2(x-2)(5x-3)#