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2 February, 10:41

How do I factor 2x^3+250

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  1. 2 February, 11:31
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    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)
  2. 2 February, 11:32
    0
    2x^3+250

    2 (x^3 + 125)

    -125 = x^3

    cuberoot (-125) = x

    x=-5
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