1. Consider the polynomial P(x) = x3 + 4x2 + k3x + 3, where k is some integer. Find all possible values of k such that P(x) has a rational root. (Clearly explain why there are no other values of k that work.)
2. Let u and v be two unit vectors such that u • v = 1/32.
(a) Prove that vectors u-v and 3u+3v are perpendicular.
(b) Find the angle between vectors 2u+6v and 3u-v.
Hint: Consider how dot product of a vector with itself is related to its length.