How do you factor $(x^{3}) - 100 = 0$ $(x^3)- 100 = 0$ ?

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How do you factor $(x^{3}) - 100 = 0$ $(x^3)- 100 = 0$ ?

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Answer 1 · 2018-01-19T21:50:12

$(x - \sqrt[3]{100}) (x^{2} + x \sqrt[3]{100} + {(\sqrt[3]{100})}^{2}) = 0$ $(x-root 3 100)(x^2+xroot3 100+ (root 3 100)^2)=0$

Explanation:

We could use the fact that $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ $a^3-b^3=(a-b)(a^2+ab+b^2)$

So we could rewrite $x^{3} - 100 = 0$ $x^3-100=0$ as
$x^{3} - {(\sqrt[3]{100})}^{3} = 0 \Rightarrow (x - \sqrt[3]{100}) (x^{2} + x \sqrt[3]{100} + {(\sqrt[3]{100})}^{2}) = 0$ $x^3-(root 3 100)^3=0=>(x-root 3 100)(x^2+xroot3 100+ (root 3 100)^2)=0$

To find the values of $x$ $x$ , you could solve the following equations:
$x - \sqrt[3]{100} = 0$ $x-root 3 100=0$ and $x^{2} + x \sqrt[3]{100} + {(\sqrt[3]{100})}^{2} = 0$ $x^2+xroot3 100+ (root 3 100)^2=0$ .

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How do you factor $(x^{3}) - 100 = 0$ $(x^3)- 100 = 0$ ?

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How do you factor $(x^{3}) - 100 = 0$ $(x^3)- 100 = 0$ ?