Factor x^4-x^3+x-1 - MathMaster

$x^{4} - x^{3} + x - 1$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

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

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

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

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

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

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

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

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

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

Factor.

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Simplify.

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Multiply $- 1$ by $1$ .

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

One to any power is one.

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

Remove unnecessary parentheses.

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

Factor x^4-x^3+x-1

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