Factor -9x^2+6x-1

$- 9 x^{2} + 6 x - 1$

Step 1

Factor $- 1$ out of $- 9 x^{2} + 6 x - 1$ .

Factor $- 1$ out of $- 9 x^{2}$ .

$- (9 x^{2}) + 6 x - 1$

Factor $- 1$ out of $6 x$ .

$- (9 x^{2}) - (- 6 x) - 1$

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

$- (9 x^{2}) - (- 6 x) - 1 (1)$

Factor $- 1$ out of $- (9 x^{2}) - (- 6 x)$ .

$- (9 x^{2} - 6 x) - 1 (1)$

Factor $- 1$ out of $- (9 x^{2} - 6 x) - 1 (1)$ .

$- (9 x^{2} - 6 x + 1)$

Step 2

Factor using the perfect square rule.

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$- ({(3 x)}^{2} - 6 x + 1)$

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

$- ({(3 x)}^{2} - 6 x + 1^{2})$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 x = 2 \cdot (3 x) \cdot 1$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 x$ and $b = 1$ .

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