Is it possible to factor $y = x^{4} + 27 x$ $y=x^4 + 27x$ ? If so, what are the factors?

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Answer 1 · 2016-06-28T07:37:19

Yes $y = x^{4} + 27 x = x (x + 3) (x^{2} - 3 x + 9)$ $y=x^4+27x=x(x+3)(x^2-3x+9)$

$y = x^{4} + 27 x$ $y=x^4+27x$

= $x (x^{3} + 27)$ $x(x^3+27)$

= $x (x^{3} + 3 x^{2} - 3 x^{2} - 9 x + 9 x + 27)$ $x(x^3+3x^2-3x^2-9x+9x+27)$

= $x (x^{2} (x + 3) - 3 x (x + 3) + 9 (x + 3))$ $x(x^2(x+3)-3x(x+3)+9(x+3))$

= $x (x + 3) (x^{2} - 3 x + 9)$ $x(x+3)(x^2-3x+9)$

Is it possible to factor y=x^4 + 27x y=x4+27xy=x^4 + 27x ? If so, what are the factors?