Factor x^5+54x-15x^3

$x^{5} + 54 x - 15 x^{3}$

Factor $x$ out of $x^{5} + 54 x - 15 x^{3}$ .

Factor $x$ out of $x^{5}$ .

$x \cdot x^{4} + 54 x - 15 x^{3}$

Factor $x$ out of $54 x$ .

$x \cdot x^{4} + x \cdot 54 - 15 x^{3}$

Factor $x$ out of $- 15 x^{3}$ .

$x \cdot x^{4} + x \cdot 54 + x (- 15 x^{2})$

Factor $x$ out of $x \cdot x^{4} + x \cdot 54$ .

$x (x^{4} + 54) + x (- 15 x^{2})$

Factor $x$ out of $x (x^{4} + 54) + x (- 15 x^{2})$ .

$x (x^{4} + 54 - 15 x^{2})$

Factor $x^{4} + 54 - 15 x^{2}$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $54$ and whose sum is $- 15$ .

$- 9, - 6$

Write the factored form using these integers.

$x ((x^{2} - 9) (x^{2} - 6))$

Rewrite $9$ as $3^{2}$ .

$x ((x^{2} - 3^{2}) (x^{2} - 6))$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$x ((x + 3) (x - 3) (x^{2} - 6))$

Remove unnecessary parentheses.

$x (x + 3) (x - 3) (x^{2} - 6)$

Factor x^5+54x-15x^3

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