Consider the set of polynomial latex: s=\{ p_1(x), p_2(x), p_3(x), p_4(x), p_5(x), p_6(x) \}, \text{where } p_1(x) = x^3+1, p_2(x) = x^3+x, p_3(x) = x^3+x^2, p_4(x) = x^2+1, p_5(x) = x^2+x, p_6(x) = x+1. s = { p 1 ( x ) , p 2 ( x ) , p 3 ( x ) , p 4 ( x ) , p 5 ( x ) , p 6 ( x ) } , where p 1 ( x ) = x 3 + 1 , p 2 ( x ) = x 3 + x , p 3 ( x ) = x 3 + x 2 , p 4 ( x ) = x 2 + 1 , p 5 ( x ) = x 2 + x , p 6 ( x ) = x + 1. find a basis of the subspace w=span(s).