How do you factor x^4 + 27x?

Jul 24, 2016

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

Explanation:

${x}^{4} + 27 x$
$= x \left({x}^{3} + 27\right)$
$= x \left({x}^{3} + {3}^{3}\right)$
As per formula ${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$
we can write
$= x \left(x + 3\right) \left({x}^{2} - 3 x + {3}^{2}\right)$
$= x \left(x + 3\right) \left({x}^{2} - 3 x + 9\right)$