P(x) = 3x^5 + 5x^4 – 4x^3 + 7x + 3
a) Find the quotient and remainder when P(x) is divided by x + 2
b) Find P(-2)
c) Find the quotient and remainder when P(x) is divided by x – 1
d) Find P(1)
f(x) = x^3 – 7x + 6
a) Find the quotient and remainder when f(x) is divided by x – 1
b) Find P(1)
c) Factor f(x) into its three linear factors
Answer the following
questions as a group and post your answers as a comment (be sure to list all group members’ names at the top of
1) How is the remainder when dividing a polynomial f(x) by x – c related to evaluating f(c)?
2) What is the significance of dividing a polynomial by x – c and having a remainder of zero?
3) For some polynomial P(x), if P(a) = 0 what else is true?
Answer the following questions without actually dividing:
4) What is the remainder when 6x1000 – 17x562 + 12x + 26 is divided by x + 1?
5) Is x – 1 a factor of x567 – 3x400 + x9 + 2?
For a given house, explore questions like “How much would you end up paying over the entire term of the mortgage, and how does this compare to the value of the house?” and “How big is the difference in monthly payments between a 15-year mortgage and a 30-year mortgage?”
A pitcher's Earned Run Average (ERA) is the mean average number of runs he gives up per nine innings pitched, which is a full game of baseball. For example, if he's pitched six innings and given up four runs, that's an average of two runs per three innings. Extending that to nine innings, he'd give up six runs, so his ERA would be 6.00 at that point.
As the season goes on and he pitches more games, his ERA will constantly change in value, but it always represents the average number of runs he would give up over nine innings of pitching. If he's given up 11 runs after pitching a total of 18 innings, his ERA would be 5.50.
I recently attended a Red Sox game, and one pitcher had an ERA of 13.50 when he came into the game. After he got one batter out, his ERA dropped to 13.00. Note that since there are three outs in an inning, one out represents a third of an inning pitched.
How many innings had that pitcher pitched before he came into the game I saw?