Factor \( v^{3}-25 v^{2}-4 v+100 \) \( v^{3}-25 v^{2}-4 v+100=\square \)

To factor the polynomial \( v^{3}-25 v^{2}-4 v+100 \), we can look for rational roots using the Rational Root Theorem. Testing potential rational roots, we find that \( v = 25 \) works, resulting in a quotient of \( v^2 - 4 \). Therefore, we can factor the polynomial as \( (v - 25)(v^2 - 4) \). The expression \( v^2 - 4 \) can be factored further using the difference of squares: \[ v^{3}-25 v^{2}-4 v+100 = (v - 25)(v - 2)(v + 2) \] This shows that we can reduce our cubic polynomial into linear factors with beautiful components. If you're looking to solve or graph this polynomial, understanding its roots can be enlightening! The real roots are \( v = 25, v = 2, \) and \( v = -2 \). These points can be crucial in sketching the graph of the cubic function. When graphed, you'll find the function crosses the x-axis at these roots, giving you insight into its behavior and any potential maxima or minima. Happy factoring!