Factor 5x^3-x^5+14x

$5 x^{3} - x^{5} + 14 x$

Step 1

Factor $- x$ out of $5 x^{3} - x^{5} + 14 x$ .

Reorder $5 x^{3}$ and $- x^{5}$ .

$- x^{5} + 5 x^{3} + 14 x$

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

$- x (x^{4}) + 5 x^{3} + 14 x$

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

$- x (x^{4}) - x (- 5 x^{2}) + 14 x$

Factor $- x$ out of $14 x$ .

$- x (x^{4}) - x (- 5 x^{2}) - x (- 14)$

Factor $- x$ out of $- x (x^{4}) - x (- 5 x^{2})$ .

$- x (x^{4} - 5 x^{2}) - x (- 14)$

Factor $- x$ out of $- x (x^{4} - 5 x^{2}) - x (- 14)$ .

$- x (x^{4} - 5 x^{2} - 14)$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$- x ({(x^{2})}^{2} - 5 x^{2} - 14)$

Step 3

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$- x (u^{2} - 5 u - 14)$

Step 4

Factor $u^{2} - 5 u - 14$ 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 $- 14$ and whose sum is $- 5$ .

$- 7, 2$

Write the factored form using these integers.

$- x ((u - 7) (u + 2))$

Step 5

Factor.

Replace all occurrences of $u$ with $x^{2}$ .

$- x ((x^{2} - 7) (x^{2} + 2))$

Remove unnecessary parentheses.

$- x (x^{2} - 7) (x^{2} + 2)$

Factor 5x^3-x^5+14x

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