Consider the polynomial function P(x) = 2x^3 - mx^2 + x - 5m. The remainder when P(x) is divided by (x - 2) is four times the remainder from dividing P(x) by (x + 1). Determine m algebraically
and show all your work.

m = 57/14 =

Step-by-step explanation:

The polynomial can be expressed as follows;

P(x) = 2·x³ - m·x² + x - 5·m

(2·x³ - m·x² + x - 5·m) ÷ (x - 2)

          2·x²

          (-m - 2)·x² + x

                   (-m - 2)·x

                      (m + 3)·x - 5·m

                      (m + 3)·x

                                      -5·m

The remainder = -5·m/(x -2)

Similarly, dividing by (x + 1) will give a remainder of -5·m/(x + 1)

But -5·m/(x -2) = 4×-5·m/(x + 1)

5/(x -2) = 20/(x + 1)

5(x + 1) = 20(x -2)

20x - 5x= 40 + 5

x = 45/15 = 3

2·3³ - m·3² + 3 - 5·m = 54 - 9m + 3 - 5m = 57 - 14m

(57 - 14m)/1 = (57 - 14m)/4

228 - 56m =57 - 14m

171 = 56m-14m =  42m

m = 171/42 = 57/14.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.