Polynomial Regression in R Part 1: Theory

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Ok i need some clarification. I understand that the p values indicates whether the model explains significant variability in y above and beyond that of other models x, x^2... but something is bugging me about my analysis.
I have the situation where model1(x): p = 4.8e-13, sum of squares =53, model2: p = 2.2e-16, sum of squares = 141. Am I right in saying that model 1 is a better fit since the sum of squares smaller, even though model1 is "significant"?

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