[QUEVS-04001]

Consider the vector space \(\Pbb_5(t)\) whose elements \(p(t)\) are polynomials in \(t\) of degree less than or equal to 4.
\[ p(t) =\alpha_0 +\alpha_1t + \alpha_2 t^2 + \alpha_3 t^3 +\alpha_4t^4\]  Consider the subspace
\(\Vsc_1\) of \(\Pbb_5(t)\) consisting of polynomials which are even functions  of  \(t\). What is the dimension of \(\Vsc_1\)?  What is the vector space \(\Vsc_2\) such that \( \Pbb_5(t) =  \Vsc_1 \oplus \Vsc_2\). Give a basis in \(\Vsc_2\).