Calculus Examples

$6 + x - x^{2}$

Step 1

Factor $- 1$ out of $6 + x - x^{2}$ .

Tap for more steps...

Step 1.1

Reorder the expression.

Tap for more steps...

Step 1.1.1

Move $6$ .

$x - x^{2} + 6$

Step 1.1.2

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

$- x^{2} + x + 6$

Step 1.2

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

$- (x^{2}) + x + 6$

Step 1.3

Factor $- 1$ out of $x$ .

$- (x^{2}) - 1 (- x) + 6$

Step 1.4

Rewrite $6$ as $- 1 (- 6)$ .

$- (x^{2}) - 1 (- x) - 1 (- 6)$

Step 1.5

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

$- (x^{2} - x) - 1 (- 6)$

Step 1.6

Factor $- 1$ out of $- (x^{2} - x) - 1 (- 6)$ .

$- (x^{2} - x - 6)$

Step 2

Factor.

Tap for more steps...

Step 2.1

Factor $x^{2} - x - 6$ using the AC method.

Tap for more steps...

Step 2.1.1

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 $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Step 2.1.2

Write the factored form using these integers.

$- ((x - 3) (x + 2))$

Step 2.2

Remove unnecessary parentheses.

$- (x - 3) (x + 2)$