Today I was given a question in class as an extra credit project. Looking at it I really have no idea where to start, but I am doing poorly in the class so the extra marks would help quite a bit. We have recently learned synthetic division and the Rational root theorem so I assume that we must use these to answer the questions. If you would be able to point me in the right direction that would be a lot of help.

Do the following things for the given equation:

y = x^10 + 4x^9 - 37x^8 - 118x^7 + 317x^6 + 608x^5 - 1067x^4 - 1058x^3 +1506x^2 + 564x - 720

Find all factors
Find all roots
Find the y-intercept
Describe the degree and shape of the graph
Graph and label all intercepts
Describe when the equation is positive and negative
Find the expression for the local max and min points