How do you factor #z^3 - 4#?
1 Answer
Apr 26, 2016
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
#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))#