How do I factorize ( break down into (x+...) (x-..) or such as those) the following:
x^3 + 10

Question

How do I factorize ( break down into (x+...) (x-..) or such as those) the following:
x^3 + 10

mathmale · Answer

It might be easier to explain this with a simpler problem.

How would you factorize x^3 - 8?
I'd change that 8 to 2^3; this is a perfect cube.

Then, x^3 - 2^3 = (x - 2)(  ?????   )    can you fill this in?

Now for x^3 + 10:  Simply rewrite 10 as a cube:$$10=(\sqrt[3]{10)}^3$$

mathmale · Answer

Then your x^3 + 10 becomes$$x^3 + (\sqrt[3]{10} )^{3}$$

Last hint:  Look up "special products and factors"