Factor 15+2x-x^2

$15 + 2 x - x^{2}$

Step 1

Factor $- 1$ out of $15 + 2 x - x^{2}$ .

Reorder the expression.

Move $15$ .

$2 x - x^{2} + 15$

Reorder $2 x$ and $- x^{2}$ .

$- x^{2} + 2 x + 15$

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

$- (x^{2}) + 2 x + 15$

Factor $- 1$ out of $2 x$ .

$- (x^{2}) - (- 2 x) + 15$

Rewrite $15$ as $- 1 (- 15)$ .

$- (x^{2}) - (- 2 x) - 1 (- 15)$

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

$- (x^{2} - 2 x) - 1 (- 15)$

Factor $- 1$ out of $- (x^{2} - 2 x) - 1 (- 15)$ .

$- (x^{2} - 2 x - 15)$

Step 2

Factor.

Factor $x^{2} - 2 x - 15$ 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 $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Write the factored form using these integers.

$- ((x - 5) (x + 3))$

Remove unnecessary parentheses.

$- (x - 5) (x + 3)$

Factor 15+2x-x^2

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