UTM Ideals Varieties and Algorithm - Chapter 1 Section 5 Exercise 4

Problem:

Solution:

Since $ h $ is a factor of $ f $ and $ g $, we have

$ f = ph $ and $ g = qh $

We have $ qf - pg = qph - pqh = qph - qph = 0 $

Therefore $ A = q $ and $ B = -p $