Let $(x+a)$ be the HCF of $x^2+px+q$ and $x^2+mx+n$. Show that $a=(q-n)/(p-m)$.
closed as off-topic by Xander Henderson, steven gregory, Leucippus, YiFan, John Omielan May 14 at 1:50
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Xander Henderson, steven gregory, Leucippus, YiFan, John Omielan
$x+a$ divides both polynomials. Hence $x=-a$ is a common root for both. Plug in $x=-a$ in both and subtract.