Math 116 Winter 06

Assignment 6 due Thursday, February 9

Chapter 2, Exercises #35, 36. Do
these by canceling and without using a calculator. However, you can leave the final result in factored form; no
need to multiply together all the factors.

Chapter 2, Exercises 38, 42, 44, 46, 55, 56. In #55, a dummy is a player with no
power.

Problem A. (Not from the
textbook)

A famous formula is (x + 1)^{N} =

_{N}C_{0}x^{N} + _{N}C_{1}x^{N-1} + _{N}C_{2}x^{N-2} + . . .
+_{ N}C_{N-1}x + _{N}C_{N}.

(a) Verify this result for N
= 2, 3, 4, and 5 by polynomial multiplication. Hint: Work it out for N = 2 first. Then multiply your result by x + 1 to get it
for n = 3. Multiply again by x + 1 to get it for N = 4, etc.

(b) As you did the multiplications you may have noticed that at
one stage in each of your multiplications you did some arithmetic that
resembled how you can add together two adjacent terms in the same row of
Pascal's triangle to get the entry in the next row that is between the two you
added. Where did this occur in
your polynomial multiplying?

(c) If you substitute
x = 1 into the famous
formula what do you get on the two sides of the formula.

(d) What if you substitute
x = -1?