How do you factor #-25x^2-70x+120#?

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Answer 1 · 2015-05-30T10:03:33

First separate out the common factor #-5# ...

#-25x^2-70x+120 = -5(5x^2+14x-24)#

Then, using a version of the AC Method, look for a pair of factors of #5*24 = 120#, whose difference is #14#...

#20 xx 6 = 120#
#20 - 6 = 14#

Then use the pair we found to split the middle term and factor by grouping...

#-5(5x^2+14x-24)#

#=-5(5x^2+20x-6x-24)#

#=-5((5x^2+20x)-(6x+24))#

#=-5(5x(x+4)-6(x+4))#

#=-5(5x-6)(x+4)#