multiplicity and zeros of a function with more on right side

Question

I got to the problem of finding the zeros and their multiplicity for $f(x)=(x^2 -5x + 6)^2$. How do you do it with all that on the right hand side? There isn't an example like that in the book chapter and it's an even numbered problem so no solution to try and work backwards (really hate those.........).

Answer 1

We have $f(x) = (x^2-5x+6)^2 = ((x-2)(x-3))^2 = (x-2)^2(x-3)^2$. Now conclude what you want.