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

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

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

Factor out the GCF of $x$ from each term in the polynomial.

Factor out the GCF of $x$ from the expression $x^{4}$ .

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

Factor out the GCF of $x$ from the expression $- 3 x^{3}$ .

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

Factor out the GCF of $x$ from the expression $- x^{2}$ .

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

Factor out the GCF of $x$ from the expression $3 x$ .

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

Since all the terms share a common factor of $x$ , it can be factored out of each term.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

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

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

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 $b = 1$ .

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

Remove unnecessary parentheses.

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