Factor P(x)=x^3+5x^2-x-5

$P (x) = x^{3} + 5 x^{2} - x - 5$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$P (x) = (x^{3} + 5 x^{2}) - x - 5$

Factor out the greatest common factor (GCF) from each group.

$P (x) = x^{2} (x + 5) - (x + 5)$

Factor the polynomial by factoring out the greatest common factor, $x + 5$ .

$P (x) = (x + 5) (x^{2} - 1)$

Rewrite $1$ as $1^{2}$ .

$P (x) = (x + 5) (x^{2} - 1^{2})$

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 $b = 1$ .

$P (x) = (x + 5) ((x + 1) (x - 1))$

Remove unnecessary parentheses.

$P (x) = (x + 5) (x + 1) (x - 1)$