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**1. Homework Statement**

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. Homework 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.