SOLUTION: Factor completely 125x^6+x^3

Question 94403: Factor completely 125x^6+x^3
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Factor completely 125x^6+x^3
:
Factor out x^3 and you have:
x^3(125x^3 + 1)
:
You should recognize (125x^3 + 1) as the sum of cubes. (125 = 5^3 and 1^3 is 1)
:
In your algebra book somewhere they should have, check the index for:
"Sum of cubes": a^3 + b^3 = (a + b)(a^2 - ab + b^2)
:
Applying this to 125x^3 + 1, we have:
(5x + 1) (25x^2 - 5x + 1)
:
Include the x^3, that we factored out earlier and we have:
x^3 (5x + 1) (25x^2 + 5x + 1)
:
Did this make sense to you?
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