Question

Which expression does not factor?

m3 + 1

m3 – 1

m2 + 1

m2 – 1

Answer 1

m^2 + 1

Reason: m^3 + 1 = (m + 1)(m^2 − m + 1), m^3 − 1 = (m − 1)(m^2 + m + 1), m^2 − 1 = (m − 1)(m + 1). m^2 + 1 has no factorization with real (or rational) coefficients.