Pre-Algebra Examples

$\frac{x^{2} + 2 x - 24}{4 - x}$

Step 1

Factor $x^{2} + 2 x - 24$ using the AC method.

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Step 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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 4) (x + 6)}{4 - x}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x - 4$ and $4 - x$ .

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Step 2.1.1

Factor $- 1$ out of $x$ .

$\frac{(- 1 (- x) - 4) (x + 6)}{4 - x}$

Step 2.1.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{(- 1 (- x) - 1 (4)) (x + 6)}{4 - x}$

Step 2.1.3

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

$\frac{- 1 (- x + 4) (x + 6)}{4 - x}$

Step 2.1.4

Reorder terms.

$\frac{- 1 (- x + 4) (x + 6)}{- x + 4}$

Step 2.1.5

Cancel the common factor.

$\frac{- 1 (- x + 4) (x + 6)}{- x + 4}$

Step 2.1.6

Divide $- 1 (x + 6)$ by $1$ .

$- 1 (x + 6)$

Step 2.2

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

$- (x + 6)$

Step 2.3

Apply the distributive property.

$- x - 1 \cdot 6$

Step 2.4

Multiply $- 1$ by $6$ .

$- x - 6$