Exr0n

• All polynomials have \((x+2)\) as a factor, and therefore can be written in the form \((x+2)f_j(x)\) where \(f_j(x)\) has degree at most \(m-1\).
• Because the \(z^0, z^1, ..., z^{m-1}\) is a spanning list of \(P_m-1(F)\), the spanning list of \(P_{m-1}(F)\) is of length \(m\).
• The original list had \(m+1\) elements, so by Axler 2.23 the list cannot be linearly independent.
• We can therefore find a non-trivial combination that equals zero, and can thus find a non-trivial combination of the original list by multiplying each vector by \((x-2)\).

#incomplete