SOLUTION: My question is 5x^3-1080 and I have to factor completely The furthest that I've gotten is 5(x^3-216) and my notes aren't really helping me. Thanks for the help, this is really

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: My question is 5x^3-1080 and I have to factor completely The furthest that I've gotten is 5(x^3-216) and my notes aren't really helping me. Thanks for the help, this is really       Log On


   

Question 565162: My question is 5x^3-1080 and I have to factor completely
The furthest that I've gotten is 5(x^3-216) and my notes aren't really helping me.
Thanks for the help, this is really confusing me.
Found 2 solutions by jim_thompson5910, mananth:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's factor x%5E3-216


x%5E3-216 Start with the given expression.


%28x%29%5E3-%286%29%5E3 Rewrite x%5E3 as %28x%29%5E3. Rewrite 216 as %286%29%5E3.


%28x-6%29%28%28x%29%5E2%2B%28x%29%286%29%2B%286%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28x-6%29%28x%5E2%2B6x%2B36%29 Multiply


So x%5E3-216 factors to %28x-6%29%28x%5E2%2B6x%2B36%29.

In other words, x%5E3-216=%28x-6%29%28x%5E2%2B6x%2B36%29

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So 5%28x%5E3-216%29 becomes 5%28x-6%29%28x%5E2%2B6x%2B36%29


This means that 5x%5E3-1080 fully factors to 5%28x-6%29%28x%5E2%2B6x%2B36%29


In other words, 5x%5E3-1080=5%28x-6%29%28x%5E2%2B6x%2B36%29
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Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
5%28x%5E3-216%29

You have to use the difference of two cubes formula
a%5E3-b%5E3=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29

5%28%28x%29%5E3-%286%29%5E3%29

5%28%28x-6%29%28x%5E2%2B6x%2B36%29%29