**Is the following proof valid? If not, what is the invalid step in the proof?**
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:- | :-
| $\phantom{=}2x^2+10x+6$
Step $1\quad$ | $=2x^2+7x+3+(3x+3)$
Step $2$ | $=2x^2+6x+x+3+3(x+1)$
Step $3$ | $=2x(x+3)+(x+3)+3(x+1)$
Step $4$ | $=(x+3)(2x+1)+3(x+1)$
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