Algebra 1 Honors

Question

A rectangular patio has an area of 2x² + 13x - 24 ft². Use factoring to find possible dimensions of the patio. The patio is to be enlarged so that each dimension is 2 ft greater than it was originally. What are the new dimensions of the patio? What is the new area of the patio?

Answer 1

The first thing we need to do is REWRITE the middle term so that a x c = 2 x -24 = -48 AND the sum of b is 13. Please see below for the steps:

2x² + 13x - 24

2x² - 3x + 16x -24

x(2x - 3) + 8(2x - 3)

SOLUTION: (x + 8)(2x - 3)