Factor -w^2+12w-35

$- w^{2} + 12 w - 35$

Step 1

Factor $- 1$ out of $- w^{2} + 12 w - 35$ .

Factor $- 1$ out of $- w^{2}$ .

$- (w^{2}) + 12 w - 35$

Factor $- 1$ out of $12 w$ .

$- (w^{2}) - (- 12 w) - 35$

Rewrite $- 35$ as $- 1 (35)$ .

$- (w^{2}) - (- 12 w) - 1 (35)$

Factor $- 1$ out of $- (w^{2}) - (- 12 w)$ .

$- (w^{2} - 12 w) - 1 (35)$

Factor $- 1$ out of $- (w^{2} - 12 w) - 1 (35)$ .

$- (w^{2} - 12 w + 35)$

Step 2

Factor.

Factor $w^{2} - 12 w + 35$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $35$ and whose sum is $- 12$ .

$- 7, - 5$

Write the factored form using these integers.

$- ((w - 7) (w - 5))$

Remove unnecessary parentheses.

$- (w - 7) (w - 5)$

Factor -w^2+12w-35

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