#1

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour x is given by x(t)=4t^2+20t+92, where t is the number of hours since 10 AM, 0t4.

a. Find an expression for the revenue per hour R as a function of x. b. Find and simplify (Rx)(t). What does this represent? c. What is the revenue per hour at noon? d. If the price were raised to $3 per hot dog with no change in the x(t) equation, which hour would produce the most revenue? Why? e. If the price were dropped to $1 per hot dog, but that price drop caused the number of sales to increase according to the function x(t)=9t2+22t+138, would the vendor make more money at the original $2 price, or at the $1 price?

#2

Examine the polynomial f(x)=6x45x39x2.

a. Use the Remainder Theorem to evaluate f(2). State your answer in term of f(2). b. How can the remainder theorem be useful? c. Use the Factor Theorem to completely factor f(x). d. Will the factor theorem ever be unsuccessful? Explain why. If so, what will cause it to be unsuccessful? e. Find all solutions to f(x)=0.