I'm trying to find the Characteristic Polynomial of a matrix. I have the worked solution to the problem, but all my polynomials seem to be the solutions I find, but multiplied by -1. I don't know what I'm doing incorrectly.

For example, I run the line"

CharacteristicPolynomial[{{-6, 4, -8}, {28, -15, 32}, {21, -12, 25}}, x]

and get

2 - 5 x + 4 x^2 - x^3

where as my book's solution is: -2 + 5 x - 4 x^2 + x^3

This is making my graphs completely upside-down. Here is the full problem:

[M] Let A = [ {-6, 4, -8}, {28, -15, a}, {21, -12, 25}] where each {} contains a column of matrix A

For each value of a in the set {32, 31.9, 31.8, 32.1, 32.2}, compute the characteristic polynomial of A and the eigenvalues. In each case, create a graph of the characteristic polynomial p(t) = det(A-tI) for 0<=t<=3. If possible, construct all graphs on one coordinate system. Describe how the graphs reveal the changes in the eigenvalues as a changes.

Any help would be greatly appreciated!