Calculus Examples

$5 - 4 x - x^{2}$

Step 1

Factor $- 1$ out of $5 - 4 x - x^{2}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $5$ .

$- 4 x - x^{2} + 5$

Step 1.1.2

Reorder $- 4 x$ and $- x^{2}$ .

$- x^{2} - 4 x + 5$

Step 1.2

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

$- (x^{2}) - 4 x + 5$

Step 1.3

Factor $- 1$ out of $- 4 x$ .

$- (x^{2}) - (4 x) + 5$

Step 1.4

Rewrite $5$ as $- 1 (- 5)$ .

$- (x^{2}) - (4 x) - 1 (- 5)$

Step 1.5

Factor $- 1$ out of $- (x^{2}) - (4 x)$ .

$- (x^{2} + 4 x) - 1 (- 5)$

Step 1.6

Factor $- 1$ out of $- (x^{2} + 4 x) - 1 (- 5)$ .

$- (x^{2} + 4 x - 5)$

Step 2

Factor.

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Step 2.1

Factor $x^{2} + 4 x - 5$ using the AC method.

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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 $- 5$ and whose sum is $4$ .

$- 1, 5$

Step 2.1.2

Write the factored form using these integers.

$- ((x - 1) (x + 5))$

Step 2.2

Remove unnecessary parentheses.

$- (x - 1) (x + 5)$