Factor -x^2+16x-55

$- x^{2} + 16 x - 55$

Step 1

Factor $- 1$ out of $- x^{2} + 16 x - 55$ .

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

$- (x^{2}) + 16 x - 55$

Factor $- 1$ out of $16 x$ .

$- (x^{2}) - (- 16 x) - 55$

Rewrite $- 55$ as $- 1 (55)$ .

$- (x^{2}) - (- 16 x) - 1 (55)$

Factor $- 1$ out of $- (x^{2}) - (- 16 x)$ .

$- (x^{2} - 16 x) - 1 (55)$

Factor $- 1$ out of $- (x^{2} - 16 x) - 1 (55)$ .

$- (x^{2} - 16 x + 55)$

Step 2

Factor.

Factor $x^{2} - 16 x + 55$ 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 $55$ and whose sum is $- 16$ .

$- 11, - 5$

Write the factored form using these integers.

$- ((x - 11) (x - 5))$

Remove unnecessary parentheses.

$- (x - 11) (x - 5)$

Factor -x^2+16x-55

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