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45 votes
Factor each and find all roots. x^3+ 27 = 0

User Fbwnd
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1 Answer

17 votes
17 votes

To factor the expression:


x^3+27

we need to notice that this is equal to:


x^3+27=x^3+3^3

then we have a sum of cubes. A sum of cubes can always be factor as:


x^3+y^3=(x+y)(x^2-xy+y^2)

Then we can factor the expression as:


x^3+27=(x+3)(x^2-3x+9)

To find the roots we equal the factor expression to zero and solve for x:


(x+3)(x^2-3x+9)=0

This equation implies that:


\begin{gathered} x+3=0 \\ or \\ x^2-3x+9=0 \end{gathered}

The first equation can be solved as:


\begin{gathered} x+3=0 \\ x=-3 \end{gathered}

The second one can be solve as:


undefined

User Apples
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