How do you factor completely #16x^3-32x^2-25x+50#?

1 Answer
Apr 26, 2016

Answer:

#16x^3-32x^2-25x+50=(4x-5)(4x+5)(x-2)#

Explanation:

Factor by grouping, then using the difference of squares identity:

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

with #a=4x# and #b=5# as follows:

#16x^3-32x^2-25x+50#

#=(16x^3-32x^2)-(25x-50)#

#=16x^2(x-2)-25(x-2)#

#=(16x^2-25)(x-2)#

#=((4x)^2-5^2)(x-2)#

#=(4x-5)(4x+5)(x-2)#