This is for integration of rational functions but there's a part I don't understand that is pure algebra.
2x + 4 = Ax(x-2) + B(x - 2) + Cx^2
In the book they use x = 0 and x = 2 to get B = -2 and C = 2, respectively. This makes perfect sense to me but they get A = -2 by
equating the coefficients of x^2 on the two sides
I really don't know what they mean by this. I know what a coefficient is but I still do not follow. Can anyone explain or show how they would do this. My book assumes a ton of knowledge from classes I took like 10 years ago
There is NO term on the left hand side of the equation, so your factors must be equal to 0. You aren't ignoring everything, you are placing values with everything, but in terms of the coefficient for your like terms, there isn't a term to equate with, that is why it is zero. The other two groups of like terms on the right side DO have terms on the left and so you put those equal to the coefficients of those like terms.