R Squared in polynomial multipleregrssion In a linear regression, we can use R-Squared to check if a model fits
But what if I have a polynomial regression with to variable $var_1$ and $var_2$ and a model that goes like $$y=x_0+ x_1\cdot var_1 + x_2\cdot var_1^2 + x_3\cdot var_2 + x_4\cdot var_2^2$$
can we use r squared to check if fits well (or adjusted r squared)
i looked up and find both answers, yes and no...
also can we say that  $$y=x_0+ x_1\cdot var_1 + x_2\cdot var_2$$ is a simple linear regression and use r squared?
if no, how can we check if a polynomial regression fits well?

It is an error to think that polynomial regression is not linear regression:
Why is polynomial regression considered a kind of linear regression?
It would also be a mistake to think that just by looking at $R^2$ you can tell whether a model fits.  The value of $R^2$ may be used in a significance test if you also know the sample size, but what is significant depends on the sample size.
The value of $R^2$ does tell you how much of the variability in the response variable is explained by the model.
