The accompanying Venn diagram shows the number of elements in region V. Use the given cardinalities to determine the number of elements in each of the other seven regions.
n(U) = 44, n(A) = 20, n(B) = 24,
n(C) = 22, n(ACB) = 8,
n(ANC) = 11, n(BNC) = 12
There are
elements in region I.

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.

i have no

the answer is  

d.

21

i did this one. so you should get it right.