Precalculus Examples

$\frac{x^{2} + x - 2}{x^{2} - 3 x - 4}$

Step 1

Factor $x^{2} + x - 2$ 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 $- 2$ and whose sum is $1$ .

$- 1, 2$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 1) (x + 2)}{x^{2} - 3 x - 4}$

Step 2

Factor $x^{2} - 3 x - 4$ using the AC method.

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Step 2.1

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 $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 1) (x + 2)}{(x - 4) (x + 1)}$