Factor x^5+5x^4-x-5

$x^{5} + 5 x^{4} - x - 5$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 2

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

$(x + 5) (x^{4} - 1)$

Step 3

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

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

Step 4

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

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

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 1$ .

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

Step 6

Factor.

Simplify.

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

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

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 $b = 1$ .

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor x^5+5x^4-x-5

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