1. Find the degree, leading term , leading coefficient , and
constant term of each polynomial
2. Use the division algorithm to write
as a sum of a polynomial and a
rational function whose denominator's degree is strictly greater than its numerator's.
3. Sketch the graph of the function f(x) = -3x^2 + 12x + 1. (Hint: Find the vertex first.)
(a) Use the division algorithm to write
as a sum of a polynomial and a rational
function whose numerator has a smaller degree than its denominator.
(b) Evaluate f(1). How does this compare with the remainder in the long division above?