Factor x^5-4x^3-x^2+4

$x^{5} - 4 x^{3} - x^{2} + 4$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{5} - 4 x^{3}) - x^{2} + 4$

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

$x^{3} (x^{2} - 4) - (x^{2} - 4)$

Factor the polynomial by factoring out the greatest common factor, $x^{2} - 4$ .

$(x^{2} - 4) (x^{3} - 1)$

Rewrite $4$ as $2^{2}$ .

$(x^{2} - 2^{2}) (x^{3} - 1)$

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 $b = 2$ .

$(x + 2) (x - 2) (x^{3} - 1)$

Rewrite $1$ as $1^{3}$ .

$(x + 2) (x - 2) (x^{3} - 1^{3})$

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 1$ .

$(x + 2) (x - 2) ((x - 1) (x^{2} + x \cdot 1 + 1^{2}))$

Factor.

Simplify.

Multiply $x$ by $1$ .

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

One to any power is one.

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

Remove unnecessary parentheses.

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

Factor x^5-4x^3-x^2+4

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