How do I factor 2x^3+250

2x^3 + 250 =

The first rule of factoring is to always try to factor a common factor from all terms. The terms here are 2x^2 and 250. They have the factor 2 in common.

= 2 (x^3 + 125)

Now you have a two-term polynomial.

The known two term polynomials that can be factored are a difference of two squares and a sum and a difference of two cubes. You obviously have a sum. x^2 and 125 are perfect cubes.

= 2 (x^2 + 5^3)

You have a sum of cubes.

Now you must follow the pattern of the factorization of a sum of cubes which is:

a^3 + b^3 = (a + b) (a^2 - ab + b^2)

If you follow that pattern, you will get

= (x + 5) (x^2 - 5x + 25)

2x^3+250

2 (x^3 + 125)

-125 = x^3

cuberoot (-125) = x

x=-5