Pre-Algebra Examples

$\frac{p^{2} - 2 p - 24}{6 - p}$

Step 1

Factor $p^{2} - 2 p - 24$ 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 $- 2$ .

$- 6, 4$

Step 1.2

Write the factored form using these integers.

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

Step 2

Cancel the common factor of $p - 6$ and $6 - p$ .

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Step 2.1

Factor $- 1$ out of $p$ .

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

Step 2.2

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

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

Step 2.3

Factor $- 1$ out of $- 1 (- p) - 1 (6)$ .

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

Step 2.4

Reorder terms.

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

Step 2.5

Cancel the common factor.

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

Step 2.6

Divide $- 1 (p + 4)$ by $1$ .

$- 1 (p + 4)$