Factoring Polynomials · Exercise 56

Consider this scenario:

Charlotte has appointed a chairperson to lead a city beautification project. The first act is to install statues and fountains in one of the city’s parks. The park is a rectangle with an area of $98x^2+105x-27$ m^2, as shown in the figure below. The length and width of the park are perfect factors of the area.

At the northwest corner of the park, the city is going to install a fountain. The area of the base of the fountain is $9x^2-25{\text{m}}^2.$ Factor the area to find the lengths of the sides of the fountain.

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Algebra and Trigonometry 2e · §1.5 Factoring Polynomials · Exercise 56