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

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Answer 1 · 2015-10-04T10:44:17

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

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

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:

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

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

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