Precalculus Examples

$\frac{3 x^{2} - 3 x - 1}{x^{2} - x - 2}$

Step 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 $- 1$ .

$- 2, 1$

Step 2

Write the factored form using these integers.

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