Question

My question states to graph each polynomial function. factor first if the expression is not in factor form.

f(x)=x^2(x+1)(x-1)

Not sure where to begin..

Answer 1

f(x)=x^2(x+1)(x-1) already nicely factorised. So the graph is a curve that will on the x-axis touch x=0, and respectively pass through x=1 and x=-1. This is because of the even and odd multiplicities. Since f is a polynomial with degree 4, both f(x) as x -> infinity or negative infinity are positive and towards infinity

Answer 2

Ok, I see where you got the x=0, -1,1. But I lost on the degree of 4? And if I start my "curve" on -1, go to 0 and curve again on 1? that might not make any sense..

Answer 3

If you multiply out all those factors you'll see that the leading term has 4 as its exponent. Thus it's a polynomial of degree 4. If you examine the limits as x -> +/- infinity you'll see that the function approaches +infinity. So at - infinity the function is positive. It crosses y=0 at x= -1 becoming negative for a while, then at x=1 it crosses y=0 again and becomes positive for all subsequent values of x.