Factor -24x+x^5+2x^3

$- 24 x + x^{5} + 2 x^{3}$

Factor $x$ out of $- 24 x + x^{5} + 2 x^{3}$ .

Factor $x$ out of $- 24 x$ .

$x \cdot - 24 + x^{5} + 2 x^{3}$

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

$x \cdot - 24 + x \cdot x^{4} + 2 x^{3}$

Factor $x$ out of $2 x^{3}$ .

$x \cdot - 24 + x \cdot x^{4} + x (2 x^{2})$

Factor $x$ out of $x \cdot - 24 + x \cdot x^{4}$ .

$x \cdot (- 24 + x^{4}) + x (2 x^{2})$

Factor $x$ out of $x \cdot (- 24 + x^{4}) + x (2 x^{2})$ .

$x (- 24 + x^{4} + 2 x^{2})$

Factor $- 24 + x^{4} + 2 x^{2}$ 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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Write the factored form using these integers.

$x ((x^{2} - 4) (x^{2} + 6))$

Rewrite $4$ as $2^{2}$ .

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

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 $b = 2$ .

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

Remove unnecessary parentheses.

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

Factor -24x+x^5+2x^3

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