Factor -x^2+19x+42

$- x^{2} + 19 x + 42$

Step 1

Factor $- 1$ out of $- x^{2} + 19 x + 42$ .

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

$- (x^{2}) + 19 x + 42$

Factor $- 1$ out of $19 x$ .

$- (x^{2}) - (- 19 x) + 42$

Rewrite $42$ as $- 1 (- 42)$ .

$- (x^{2}) - (- 19 x) - 1 (- 42)$

Factor $- 1$ out of $- (x^{2}) - (- 19 x)$ .

$- (x^{2} - 19 x) - 1 (- 42)$

Factor $- 1$ out of $- (x^{2} - 19 x) - 1 (- 42)$ .

$- (x^{2} - 19 x - 42)$

Step 2

Factor.

Factor $x^{2} - 19 x - 42$ 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 $- 42$ and whose sum is $- 19$ .

$- 21, 2$

Write the factored form using these integers.

$- ((x - 21) (x + 2))$

Remove unnecessary parentheses.

$- (x - 21) (x + 2)$

Factor -x^2+19x+42

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