A "degree four" polynomial is a mathematical expression that includes terms up to the fourth power of a variable, typically represented as ax^4 + bx^3 + cx^2 + dx + e . In this expression, a, b, c, d, and e are constants, and a cannot be zero, as that would reduce the degree of the polynomial. Degree four polynomials can have up to four roots, which are the values of x that make the polynomial equal to zero. These roots can be real or complex numbers, and the graph of a degree four polynomial can have various shapes, including up to three turning points, depending on the coefficients.