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Mathematics
12 February, 18:42
How do I factor 2x^3+250
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Asia Casey
12 February, 18:45
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2x^3+250
2 (x^3 + 125)
-125 = x^3
cuberoot (-125) = x
x=-5
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Dale Hebert
12 February, 18:50
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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)
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