Tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 15 minutes. Tours for the White House leave every 20 minutes. How often do the tours leave at the same time?

60 minutes

Step-by-step explanation:

To solve for the above question, we use the Lowest Common Multiple Method

We are told in the question that:

Tours for the National Capitol leave every 15 minutes. Tours for the White House leave every 20 minutes.

Find and list multiples of each number of minutes until the first common multiple is found. This is the lowest common multiple.

Multiples of 15:

15, 30, 45, 60, 75, 90

Multiples of 20:

20, 40, 60, 80, 100

Therefore,

LCM(15, 20) = 60

Therefore, the tours leave at the same time every 60 minutos

(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