Compare the nutrition labels of these three options to select the healthiest choice.
nutrition facts
serving size 1 muffin
nutrition facts
serving size 1 pastry
amount per serving
calories 274
daily value
total fat 4.49
saturated fat 1.089
cholesterol omg
sodium 313mg
total carbohydrate 52 39
dietary fiber 4 39
total sugars 5.689
nutrition facts
serving size 1 granola bar
amount per serving
calories 101
% daily value
total fat 3.299
saturated fat 0.729
cholesterol 5.6mg
sodium 232.05mg
total carbohydrate 15.469
dietary fiber 0.849
total sugars 1.589
amount per serving
calories 131.15
daily value
total fat 1.599
saturated fat 0.479
cholesterol omg
sodium 177.59mg
total carbohydrate 28.99
dietary fiber 1.859
total sugars 3.09

a. -0.3 > -0.33

6 spoons of sugar for every 21 cups of flour

step-by-step explanation:

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.