Question

Show with suitable examples, that the sum of two monic polynomial need not be monic​

Answer 1

Answer:

Must the sum of two monic polynomials always be monic?

Let’s add the two monic polynomials from above:

x² + 7x + 14

y² + 8y – 28

——————————

x² + y² + 7x + 8y – 14

This is NOT monic because it has two variables

So, to answer your question, the sum of two monic polymonials MIGHT be monic, but it MIGHT NOT.