In the standard basis of P3 (i.e. {1,x,x^2}) p(x)=3-2x+5x^2, that is, it has coordinates p=(3,-2,5). Find the coordinates of this vector (polonomial) in the basis {1-x,1+x,x^2-1}

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Solution. Suppose that p(x)=3-2x+5x^2=a(1-x)+b(1+x)+c(x^2-1), then (a,b,c) should be the coordinates of this vector p(x). So if we can ...

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