Write as a Set of Linear Factors x^4-9x^3-x^2+9x

$x^{4} - 9 x^{3} - x^{2} + 9 x$

Step 1

Factor $x$ out of $x^{4} - 9 x^{3} - x^{2} + 9 x$ .

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

$x \cdot x^{3} - 9 x^{3} - x^{2} + 9 x$

Factor $x$ out of $- 9 x^{3}$ .

$x \cdot x^{3} + x (- 9 x^{2}) - x^{2} + 9 x$

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

$x \cdot x^{3} + x (- 9 x^{2}) + x (- x) + 9 x$

Factor $x$ out of $9 x$ .

$x \cdot x^{3} + x (- 9 x^{2}) + x (- x) + x \cdot 9$

Factor $x$ out of $x \cdot x^{3} + x (- 9 x^{2})$ .

$x (x^{3} - 9 x^{2}) + x (- x) + x \cdot 9$

Factor $x$ out of $x (x^{3} - 9 x^{2}) + x (- x)$ .

$x (x^{3} - 9 x^{2} - x) + x \cdot 9$

Factor $x$ out of $x (x^{3} - 9 x^{2} - x) + x \cdot 9$ .

$x (x^{3} - 9 x^{2} - x + 9)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$x ((x^{3} - 9 x^{2}) - x + 9)$

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

$x (x^{2} (x - 9) - (x - 9))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 9$ .

$x ((x - 9) (x^{2} - 1))$

Step 4

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

$x ((x - 9) (x^{2} - 1^{2}))$

Step 5

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 $b = 1$ .

$x ((x - 9) ((x + 1) (x - 1)))$

Remove unnecessary parentheses.

$x ((x - 9) (x + 1) (x - 1))$

Remove unnecessary parentheses.

$x (x - 9) (x + 1) (x - 1)$