Topics:
• Synthetic division (a short way to do long division when dividing by x-c)
• Roots, factors, and remainders: the Remainder Theorem and the Factor Theorem
SUMMARY: For any polynomial f(x), he following three things are equivalent:
f(c) = 0 (c is a root of f(x)
(x-c) is a factor of f(x)
The remainder is 0 when you divide f(x) by x-c
• Polynomial graphs: see below
Facts about polynomial graphs:
• The domain of a polynomial is the whole real line
• The graph of a polynomial is continuous – no breaks or jumps
• The graph of a polynomial does not have any corners
• For a polynomial of degree n, there are at most n roots (which are the same as the x-intercepts of its graph) and there are at most n-1 local maxima or minima. (We will discuss this next time.)
• The end behavior of the graph is determined by the leading term of the polynomial.
Homework:
• Reread and review the Observations and the examples discussed in class.
• Finish the assigned problems from Session 8
• In Session 9, do the assigned problems from 9.1, 9.2, and 9.3
• Do the Warm-Up which is in WeBWorK this time- due tomorrow by 11 PM! Start early.
• Do theWeBWorK – a short assignment – due tomorrow by 11 PM!
