How is the process for adding two polynomials like the process for how adding two integers? How is it different?

Answer 1

add 423 + 26
4*10^2 + 2*10^1 + 3 *10^0 + 2*10^1 + 6*10^0
combine like terms
= 4*10^2 + 4*10^1 + 9 *10^0
now if it is just numbers, we can say 10^2 = 100 and 10^1 = 10 and 10^0=1
so you have
400 + 40 + 9 = 149
however if it were
4 x^2 + 2 x + 3 + 2 x + 6
combine like terms
4 x^2 + 4 x + 9
I can not take that next step expressing x^2 = something times x
because the first problem had x^2 = 100 , x = 10 so x^2 = 10 x