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

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

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 2

Factor the polynomial by factoring out the greatest common factor, $x - 3$ .

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

Step 3

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

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

Step 4

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 $b = 1$ .

$(x - 3) ((x + 1) (x - 1))$

Remove unnecessary parentheses.

$(x - 3) (x + 1) (x - 1)$