Describe the zero vector (the additive identity) of the vector space. R6 Solution The zero vector is the polynomial 0(x) such that p(x) + 0(x) = p(x) and 0(x) + p(x) = p(x). Since polynomial addition is equivalent to adding like coefficients, 0(x) must have every coefficient be zero. Hence, 0(x) = 0 + 0x + 0x 2 + 0x 3 . Equivalently, 0(x) = 0..