Answer:
4 units ...................
Given:
The expression is:

It leaves the same remainder when divided by x -2 or by x+1.
To prove:

Solution:
Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).
Let the given polynomial is:

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that
...(i)
Substituting
in the given polynomial.


Substituting
in the given polynomial.



Now, substitute the values of P(2) and P(-1) in (i), we get




Divide both sides by 3.


Hence proved.
Given the question:
The manager of a baseball team has 15 players to choose from for his
9-person batting order. How many different ways can he arrange the
players in the lineup?
5,005
362,880
3,603,600
1,816,214,400
The number of was in which a smaller group is choosing from a bigger group is given by the bigger number combination the smaller number.

Here, we want to choose a 9-person batting order from a team of 15 players. This is given by:
- 3x + 2x + 5 + 5x + 15 = 180 [angles on a line add to 180 degrees]
- 10x + 20 = 180 [combine like terms]
- 10x = 160 [subtract 20 from both sides]
- x = 16 [divide both sides by 10]
Arc AB measures 3(16) = 48 degrees.
Arc BC measures 2(16) + 5 = 41 degrees.