How do you factor x3−4?

1 Answer
Jim H
Apr 16, 2015

This cannot be factored using integers.

This cannot be factored using rational numbers.

This can be factored using the irrational number 3√4

x3−4=x3−(3√4)3=(x−3√4)(x2+x3√4+(3√4)2)
The quadratic above cannot be factored using real numbers.

Using Imaginary numbers we can solve: x2+x3√4+(3√4)2=0 (Use the quadratic formula or complete the square.)

And then we can factor further:

(x−3√4)(x−(3√42+3√4√32i))(x−(3√42−3√4√32i))

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