Select the correct answer from each drop-down menu. Use the remainder theorem to verify this statement.
(x+5) is a factor of the function f(x) = x^3 + 3x^2 - 25x - 75
1. Find the (product, quotient, difference, sum) of f(x) and x + 5
2. The (quotient, remainder, sum, discriminant) of this operation is 0
3. Therefore, (x+5) is (not a factor, the opposite, a factor, the simplified form) of function f
4. So f ([-75, 5, -5, 75)] = 0

1. quotient

2.remainder

3. a factor

4. 5

Step-by-step explanation:

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step-by-step explanation:

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.