Mackenzie's ice cream shop lets customers choose 2 toppings from the list below to add to their ice cream:

Hot fudge

Sprinkles

Caramel

Strawberries

Whipped cream

Chocolate chips

How many groups of 2 different toppings can go on

an order of ice cream?

Explanation:

There are 6 toppings and we pick two different ones. If order mattered, then there would be 6*5 = 30 permutations. However, order doesn't matter. So we divide that result by 2 and we get 30/2 = 15 combinations.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0