Answer
See below.
Work Step by Step
Use Theorem 4.2.1, results from previous exercises, and Theorem 4.2.2,
we have:
1. $-2,3,4,r$ are rational numbers,
2. $r^2, -2r, 3r^2$ are rational numbers,
3. Thus $3r^2-2r+4$ is a rational number.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.