How do you factor #z^3 - 4#?

1 Answer
George C.
Apr 26, 2016

#z^3-4 = (z-root(3)(4))(z^2+root(3)(4)z+2root(3)(2))#

Explanation:

This can be factored as a difference of cubes.

The difference of cubes identity can be written:

#a^3-b^3 = (a-b)(a^2+ab+b^2)#

We can use this with #a=z# and #b=root(3)(4)# as follows:

#z^3-4#

#= z^3-(root(3)(4))^3#

#=(z-root(3)(4))(z^2+root(3)(4)z+root(3)(16))#

#=(z-root(3)(4))(z^2+root(3)(4)z+2root(3)(2))#

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