### Home > INT3 > Chapter 12 > Lesson 12.2.1 > Problem 12-86

12-86.

Factor and simplify each expression below.

Factor and then reduce.

For the numerator, what numbers multiply to

and add to ? **Diamond Pattern, top negative 6, x squared, bottom, negative 5, x.**Put these numbers in a generic rectangle (these create your "middle term") along with the first and last terms.

**Added to diamond problem, left, negative 6, x right, 1, x. 2 by 2 rectangle added, interior labeled as follows: top left, 2, x squared, top right, 1, x, bottom left, negative 6, x, bottom right, negative 3.**

Now find the greatest common factors of each row and column.See the generic rectangle.

**Added to rectangle, left edge, x minus 3, bottom edge, 2, x, + 1.**Now factor the denominator and simplify.