How do u factor (x^3)-8?

Answer

There is a “formula”.

a^3 – b^3 = ( a – b ) ( a^2 + ab + b^2 ).

You can multiply out the Right hand side expression and you will see that it “reduces” to the left hand side expression.

In your question, just set a = x and b = 2. Indeed,

x^3 – 8
= x^3 – 2^3
= ( x – 2 ) ( x^2 + 2x + 2^2 )
= ( x – 2 ) ( x^2 + 2x + 4 )

Done.

Hope this helped

🙂

P/S : if you really wanted to factorize ” ( x^2 + 2x + 4 ) ” there is a way… but NOT in integer coefficents. Indeed
( x^2 + 2x + 4 ) = ( x + 1 + sqrt(3) i )*( x + 1 – sqrt(3) i )

where i = sqrt ( -1 ) = a complex number.

This factorization is possible in the “complex domain”.