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

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

Step 1

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

Raise $x$ to the power of $1$ .

$x^{1} - x^{2} + x^{3} - x^{4}$

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - x^{2} + x^{3} - x^{4}$

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

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

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

$x \cdot 1 + x (- x) + x \cdot x^{2} - x^{4}$

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

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

Factor $x$ out of $x \cdot 1 + x (- x)$ .

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

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

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

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

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

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.

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

Step 5

Factor.

Factor $- 1$ out of $- x + 1$ .

Factor $- 1$ out of $- x$ .

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

Rewrite $1$ as $- 1 (- 1)$ .

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

Factor $- 1$ out of $- (x) - 1 (- 1)$ .

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

Remove unnecessary parentheses.

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

Step 6

Factor.

Factor out negative.

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

Remove unnecessary parentheses.

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

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

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