At the annual dog show, Chantel noticed that there were three more Scotties than Schnauzers. She also realized that the number of Wirehaired Terriers was five less than twice the number of Schnauzers. If there
were 78 dogs in all (counting Schnauzers, Scotties, and Wirehaired Terriers), how many Schnauzers were
there? Write and solve an equation.

9514 1404 393

Step-by-step explanation:

Each of the quantities is described in terms of the number of Schnauzers, and that is the number we are asked for. It is convenient to write an equation for the number of Schnauzers. We choose to use s for the variable representing that number.

  s = # of Schnauzers

  s+3 = # of Scotties, 3 more than the number of Schnauzers

  2s-5 = # of Wire-haired Terriers, 5 less than twice the number of Schnauzers

The total number of dogs is then ...

  (s+3) +(s) +(2s-5) = 78

  4s -2 = 78 . . . . simplify

  4s = 80 . . . . . . add 2

  s = 20 . . . . . . . divide by 4

There were 20 Schnauzers at the dog show.

(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