Taking pre-calc and it's been years since I took college algebra,
I need to find the zeros and graph behavior of $f(x) = -3(x-1)^2(x^2-4)$.
I know it's $(-3(x-1)^2)(x+2) (x-2)$, but in order to find the degree of the polynomial, I need to expand which is where I'm currently stuck
The zeros would be $1$, $2$ and $-2$
We have $$(x-1)^2(x^2-4)=(x^2-2x+1)(x^2-4)=x^2(x^2-2x+1)-4(x^2-2x+1)=x^4-2x^3+x^2-4x^2+8x-4=x^4-2x^3-3x^2+8x-4$$