Explore tangent lines and conics of polynomials through a simplified high school approach using polynumbers and bipolynumbers in this 36-minute mathematics lecture. Begin by defining constant, linear, quadratic, cubic, quartic, and quintic polynumbers based on their degree. Discover subtle shifts in the Taylor bipolynumber to find polynomial Taylor expansions at a point c, and use this knowledge to define first, second, and subsequent tangents. Learn how these concepts are applied to compute polynomial value approximations. Delve into topics such as truncating polynumbers, defining tangents at various points, using translation for additional tangents, and performing approximate evaluations. Conclude with an exploration of Taylor expansions and a practical exercise to reinforce your understanding.