How do you factor #4(x^3)-8(x^2)-25x+50#?

1 Answer
George C.
Aug 29, 2016

#4x^3-8x^2-25x+50=(2x-5)(2x+5)(x-2)#

Explanation:

The difference of squares identity can be written:

#a^2-b^2=(a-b)(a+b)#

We use this with #a=2x# and #b=5# later...

#color(white)()#
Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping:

#4x^3-8x^2-25x+50#

#=(4x^3-8x^2)-(25x-50)#

#=4x^2(x-2)-25(x-2)#

#=(4x^2-25)(x-2)#

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

#=(2x-5)(2x+5)(x-2)#

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