Vector Spaces & Bases · Hard problem

Every polynomial $p$ splits uniquely as $p = p_{\text{even}} + p_{\text{odd}}$, where $p_{\text{even}}(x) = \tfrac{p(x)+p(-x)}{2}$ and $p_{\text{odd}}(x) = \tfrac{p(x)-p(-x)}{2}$. For $p(x) = x^3+2x^2-3x+5$, find the coefficient of $x$ in $p_{\text{odd}}$.