Factor R(x)=(x^2+4x-32)/(x^2-2x-8)

$R (x) = \frac{x^{2} + 4 x - 32}{x^{2} - 2 x - 8}$

Step 1

Factor $x^{2} + 4 x - 32$ 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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Write the factored form using these integers.

$R (x) = \frac{(x - 4) (x + 8)}{x^{2} - 2 x - 8}$

Step 2

Factor $x^{2} - 2 x - 8$ 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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Write the factored form using these integers.

$R (x) = \frac{(x - 4) (x + 8)}{(x - 4) (x + 2)}$

Step 3

Reduce the expression $\frac{(x - 4) (x + 8)}{(x - 4) (x + 2)}$ by cancelling the common factors.

Cancel the common factor.

$R (x) = \frac{(x - 4) (x + 8)}{(x - 4) (x + 2)}$

Rewrite the expression.

$R (x) = \frac{x + 8}{x + 2}$

Factor R(x)=(x^2+4x-32)/(x^2-2x-8)

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