Let P2 = {ax^2 + bx + c | a, b, c R} be the vector space of polynomials of degree at most 2.

Let U be a subset of P2 defined by U = {p(x) P2 | p(26) = 0}.

Show that U is a subspace of P2 using the Subspace Test.

Show that U = Span({26x x^2 , 26 x})

Explain why {26x x^2 , 26 x} is a basis of U.

Explain why {26x x^2 , 26 x, 26} is a basis of P2