Question: 1. Let p(x) = x5 + 8x4 - 30x3 + 30x2 - 31x + 22. What is the relationship between p(x) and f(x)=5x4 + 32x3 - 90x2 + 60x - 31? What do the values of p(1) and p(2) tell you about the values of f(x)?
2. Let p(x) be a seventh-degree polynomial with 7 distinct zeros. How many zeros does p'(x) have?