1. The problem statement, all variables and given/known data Let Matrix A = [2, 1, 0, 2] [-1, 0, -1, 0] [2, 1, 0, 1] [1, 0, -1, 1] Find it's transitional matrix C and diagonal matrix D such that A = CDC^-1. 2. Relevant equations 3. The attempt at a solution I find the determinant of A-tI and set it equal to 0 to get the characteristic polynomial: t^4 - 3x^3 + 3x^2 - 2. How can I quickly factor polynomials of degree 3 or 4 like this to solve for the eigenvalues? We are not allowed to use calculators or programs on our exam, and we are limited on time. The rest of the process I understand. Thanks in advance for the help.