Chapter 4 Quadratic Functions and Factoring - 4.8 Use the Quadratic Formula and the Discriminant - 4.8 Exercises - Skill Practice - Page 296: 29

$$p=-3,\:p=-5$$

Solving the equation using the quadratic formula, we find: $$p_{1,\:2}=\frac{-40\pm \sqrt{40^2-4\cdot \:5\cdot \:75}}{2\cdot \:5} \\ p=-3,\:p=-5$$ Checking by factoring the expression, we find: $$5\left(p^2+8p+15\right) \\ 5\left(p+3\right)\left(p+5\right)$$