Ariel wants to find out the most popular theme for spirit week at school. she cannot decide between two methods. option 1: she will poll each student who leaves the gym after sports practice option 2: she will randomly poll three students from each first-period class which statement about the methods is true? a. option 1 is biased b. option 2 is biased c. neither is biased d. both are biased

Option 1 says poll each student who leaves the gym after sports practice . It means she will just poll each student leaving the gym , So it will be a biased method for selecting , because the students from Sports cannot be the representative of all students , it will not be fair for other students.

Option 2 says she will randomly poll three students from each first-period class. Selecting randomly is again an unbiased method , because randomly she can select anyone , without being biased to anyone.

Hence , neither of the method is biased.

Option A is correct, first option is BIASED

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.