SOLUTION: Hi! please help me factor this polynomial completely : {{{n^5+216n^2}}} i know how to solve it up to the part {{{n^2(n^3+216)}}} but i do not know how to factor it completely

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi! please help me factor this polynomial completely : {{{n^5+216n^2}}} i know how to solve it up to the part {{{n^2(n^3+216)}}} but i do not know how to factor it completely       Log On


   

Question 586082: Hi! please help me factor this polynomial completely : n%5E5%2B216n%5E2
i know how to solve it up to the part n%5E2%28n%5E3%2B216%29 but i do not know how to factor it completely
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how you factor n%5E3%2B216


n%5E3%2B216 Start with the given expression.


%28n%29%5E3%2B%286%29%5E3 Rewrite n%5E3 as %28n%29%5E3. Rewrite 216 as %286%29%5E3.


%28n%2B6%29%28%28n%29%5E2-%28n%29%286%29%2B%286%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%28n%2B6%29%28n%5E2-6n%2B36%29 Multiply


So n%5E3%2B216 factors to %28n%2B6%29%28n%5E2-6n%2B36%29.

In other words, n%5E3%2B216=%28n%2B6%29%28n%5E2-6n%2B36%29



This means that n%5E5%2B216n%5E2 completely factors to n%5E2%28n%2B6%29%28n%5E2-6n%2B36%29
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