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

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

Step 1

Factor $x$ out of $x^{4} - x^{3} - x + x^{2}$ .

Factor $x$ out of $x^{4}$ .

$x \cdot x^{3} - x^{3} - x + x^{2}$

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

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

Factor $x$ out of $- x$ .

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

Factor $x$ out of $x^{2}$ .

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

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

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

Factor $x$ out of $x (x^{3} - x^{2}) + x \cdot - 1$ .

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

Factor $x$ out of $x (x^{3} - x^{2} - 1) + x \cdot x$ .

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

Step 2

Reorder terms.

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

Step 3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 4

Factor.

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

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

Remove unnecessary parentheses.

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