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Find a vector space complement to $\mathbb{R}(1 + x + x^2) + \mathbb{R}(x - x^2 - x^3)$ in $\mathbb{R}[x]\le_3$. (This is referring to the set of polynomials with degree less than or equal to 3.)

I am not sure I completely understand the process of finding vector space complements and it would be good to have one example of how to do it! Thanks for your help.

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    What is $\,\Bbb R(1+x+x^2)\,$? The ideal generated by the polynomial $\,1+x+x^2\,$? Or the scalar multiples of this polynomial? Or something else?2012-09-27
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    Ah I apologise, it refers to scalar multiples of the polynomial, from the real field. Thanks for the clarification.2012-09-27

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