Why degrees are equal if polynomial are equal? Two polynomial f(x) and g(x) are equal then their degrees are equal. This is a very trivial statement and it shouldn't worry me much but it is.
I get an intuitive idea why they should be equal. Their graphs wouldn't coincide for unequal degrees. But what if somehow the coefficients make f(x) = g(x) for all values of x?
Is there a more rigorous proof for this statement?