Factor 18x-11x^3+x^5

$18 x - 11 x^{3} + x^{5}$

Step 1

Factor $x$ out of $18 x - 11 x^{3} + x^{5}$ .

Factor $x$ out of $18 x$ .

$x \cdot 18 - 11 x^{3} + x^{5}$

Factor $x$ out of $- 11 x^{3}$ .

$x \cdot 18 + x (- 11 x^{2}) + x^{5}$

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

$x \cdot 18 + x (- 11 x^{2}) + x \cdot x^{4}$

Factor $x$ out of $x \cdot 18 + x (- 11 x^{2})$ .

$x \cdot (18 - 11 x^{2}) + x \cdot x^{4}$

Factor $x$ out of $x \cdot (18 - 11 x^{2}) + x \cdot x^{4}$ .

$x (18 - 11 x^{2} + x^{4})$

Step 2

Factor $18 - 11 x^{2} + x^{4}$ 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 $18$ and whose sum is $- 11$ .

$- 9, - 2$

Write the factored form using these integers.

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

Step 3

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

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

Step 4

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 $b = 3$ .

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

Remove unnecessary parentheses.

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

Factor 18x-11x^3+x^5

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