Factor P(x)=x^5-9x^3

$P (x) = x^{5} - 9 x^{3}$

Step 1

Factor $x^{3}$ out of $x^{5} - 9 x^{3}$ .

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

$P (x) = x^{3} x^{2} - 9 x^{3}$

Factor $x^{3}$ out of $- 9 x^{3}$ .

$P (x) = x^{3} x^{2} + x^{3} \cdot - 9$

Factor $x^{3}$ out of $x^{3} x^{2} + x^{3} \cdot - 9$ .

$P (x) = x^{3} (x^{2} - 9)$

Step 2

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

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

Step 3

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 $b = 3$ .

$P (x) = x^{3} ((x + 3) (x - 3))$

Remove unnecessary parentheses.

$P (x) = x^{3} (x + 3) (x - 3)$