How do you factor #x^3 - 24x^2 + 192x - 512#?

1 Answer
George C.
Oct 4, 2015

Notice that the leading and trailing terms are both perfect cubes, so try and find that:

#x^3-24x^2+192x-512 = (x-8)^3#

Explanation:

In the general case #(a+b)^3 = a^3+3a^2b+3ab^2+b^3#

Notice that #x^3# is a perfect cube and #-512 = (-8)^3# is also a perfect cube.

So try #a = x# and #b = -8# to find:

#(x-8)^3 = x^3 + 3x^2(-8) + 3x(-8)^2 + (-8)^3#

#=x^3-24x^2+192x-512#

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