Question

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

Answer 1

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:\[10=(\sqrt[3]{10)}^3\]

Answer 2

Then your x^3 + 10 becomes\[x^3 + (\sqrt[3]{10} )^{3}\]

Last hint: Look up "special products and factors"