Simplify (x^2-2x-24)÷(-x+6)

$(x^{2} - 2 x - 24) \div (- x + 6)$

Rewrite the division as a fraction.

$\frac{x^{2} - 2 x - 24}{- x + 6}$

Factor $x^{2} - 2 x - 24$ 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 $- 24$ and whose sum is $- 2$ .

$- 6, 4$

Write the factored form using these integers.

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

Simplify terms.

Cancel the common factor of $x - 6$ and $- x + 6$ .

Factor $- 1$ out of $x$ .

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

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

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

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

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

Cancel the common factor.

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

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

$- 1 (x + 4)$

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

$- (x + 4)$

Apply the distributive property.

$- x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$- x - 4$

Simplify (x^2-2x-24)÷(-x+6)

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