How do you factor the expression $x^{4} + 216 x$ $x^4+216x$ ?

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Answer 1 · 2015-12-21T01:29:23

Factor out the common factor and then look for a familiar form.
Answer is : $x (x + 6) (x^{2} - 6 x + 36) .$ $x(x+6)(x^2-6x+36).$

Factoring : $x^{4} + 216 x$ $x^4+216x$

Always look for a common factor, here it's an $x .$ $x.$ We get:

$x (x^{3} + 216)$ $x(x^3+216)$

Lucky for us, 216 is a perfect cube:

$x (x^{3} + 6^{3})$ $x(x^3+6^3)$

So it's a sum of cubes and we can use the formula:

$x (x + 6) (x^{2} - 6 x + 6^{2}) =$ $x(x+6)(x^2-6x+6^2)=$

$x (x + 6) (x^{2} - 6 x + 36) .$ $x(x+6)(x^2-6x+36).$

You can check that the last quadratic doesn't factor.

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How do you factor the expression x4+216xx^4+216x?