How do you factor # x^3-7#?

1 Answer
Shwetank Mauria
Feb 19, 2016

Factors are #(x−root(3)7)(x^2+root(3)7*x+(root(3)49))#

Explanation:

One well known identity is #(a^3-b^3)=(a-b)(a^2+ab+b^2)#.

Using this and as expressing #x^3−7# as difference cubes, it is

#(x^3−(root(3)7)^3)# - Hence factors are

#(x−root(3)7)(x^2+root(3)7*x+(root(3)7)^2)# or

#(x−root(3)7)(x^2+root(3)7*x+(root(3)49))#

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