Could someone me ? i am completely lost on how to figure out this problem.
use synthetic division to show that x is a solution for the third degree polynomial equation and use the result to factor the polynomial completely. list all real solutions of the equation
x^3 - 57x - 56 = 0, x = -1
x = (smallest value)
x =
x = (largest value)

X^3 - 57x - 56=0⇒ x(x^2-57)= 56

Verify if  x= - 1 is a solution of this equation.
(-1)* [(-1)^2 - 57]=56
(-1)[1 - 57] = 56
(-1)*(-56) = 56

56 =2*28 = (-2)*(-28) = 4*14 = (- 4)*(-14) = 8*7= (-8)*(-7)
x=8 ⇒ 8*(64-57)=56            ok⇒ x=8 is a solution
x= -7 ⇒ (-7)*(49-57)=56        ok  ⇒ x= - 7 is a solution

the smallest x= -7 
                    x= - 1
the largest   x= 8

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

the answer is 18.