We can use the Pythagorean theorem, which states that for a right triangle with legs of lengths a and b, and hypotenuse of length c, the following relationship holds:
a² + b² = c²
In this case, the lengths of the legs of the right triangle are 2x + 3 and 4x - 1. We can use these values to set up the equation:
(2x + 3)² + (4x - 1)² = c²
Simplifying the left-hand side:
4x² + 12x + 9 + 16x² - 8x + 1 = c²
20x² + 4x + 10 = c²
Therefore, the polynomial equivalent to c² is C) 20x² + 4x + 10.