[QUE/VS-04002]

Consider the vector space \(P_5(t)\) 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 \(V_1\) of \(P_5(t)\) consisting of polynomials  which are even functions of  \(t\). What is the dimension of \(V_1\)?  What is the vector space \(V_2\) such
that \( P_5(t) =  V_1 \oplus V_2\). What is dimension of quotient space \(P(t)/V_1\)? Give a basis for \(P(t)/ V_1\).