1. The question asks about the hardest equation to factor. 2. Factoring difficulty depends on the type and degree of the polynomial. 3. Generally, higher degree polynomials (degree 5 or more) with no obvious roots or patterns are hardest to factor. 4. For example, the general quintic polynomial $$ax^5 + bx^4 + cx^3 + dx^2 + ex + f$$ has no general formula for roots and is very hard to factor. 5. Special cases like cyclotomic polynomials or irreducible polynomials over rationals are also very hard. 6. In summary, there is no single "hardest" equation, but high-degree polynomials without special structure are the most challenging to factor.