Factor -x^2+3x+40

$- x^{2} + 3 x + 40$

Step 1

Factor $- 1$ out of $- x^{2} + 3 x + 40$ .

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

$- (x^{2}) + 3 x + 40$

Factor $- 1$ out of $3 x$ .

$- (x^{2}) - (- 3 x) + 40$

Rewrite $40$ as $- 1 (- 40)$ .

$- (x^{2}) - (- 3 x) - 1 (- 40)$

Factor $- 1$ out of $- (x^{2}) - (- 3 x)$ .

$- (x^{2} - 3 x) - 1 (- 40)$

Factor $- 1$ out of $- (x^{2} - 3 x) - 1 (- 40)$ .

$- (x^{2} - 3 x - 40)$

Step 2

Factor.

Factor $x^{2} - 3 x - 40$ 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 $- 40$ and whose sum is $- 3$ .

$- 8, 5$

Write the factored form using these integers.

$- ((x - 8) (x + 5))$

Remove unnecessary parentheses.

$- (x - 8) (x + 5)$

Factor -x^2+3x+40

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