Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.2 - Page 169: 26

See below.

Use Theorem 4.2.1, results from previous exercises, and Theorem 4.2.2, we have: 1. $-7, 5, 8,s$ are rational numbers, 2. $s^2, s^3, 8s^2, 5s^3$ are rational numbers, 3. Thus $5s^3+8s^2-7$ is a rational number.