Question 245743


{{{x^3+64}}} Start with the given expression.



{{{(x)^3+(4)^3}}} Rewrite {{{x^3}}} as {{{(x)^3}}}. Rewrite {{{64}}} as {{{(4)^3}}}.



{{{(x+4)((x)^2-(x)(4)+(4)^2)}}} Now factor by using the sum of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">sum of cubes formula</a> is {{{A^3+B^3=(A+B)(A^2-AB+B^2)}}}



{{{(x+4)(x^2-4x+16)}}} Multiply


-----------------------------------

Answer:


So {{{x^3+64}}} factors to {{{(x+4)(x^2-4x+16)}}}.



In other words, {{{x^3+64=(x+4)(x^2-4x+16)}}}



So to find the roots of {{{x^3+64}}}, just find the roots of {{{(x+4)(x^2-4x+16)}}}. In other words, solve the equation:



{{{(x+4)(x^2-4x+16)=0}}}