Atortoise challenges a hare to a four-hour race. the hare is so confident of winning that he allows the tortoise to start with a 10-mile lead. the hare runs at a speed of 14 miles per hour, but stops for a two-hour nap in the middle of the race. the tortoise plods along at 4 miles per hour the whole race. who gets farther in four hours?

Count the distances that a tortoise and a hare completed.

1. Tortoise. The speed of the tortoise is constant and equal to 4 miles per hour. Then in 4 hours the tortoise completed 4·4=16 miles. It has a 10-mile lead, then the distance that the tortoise completed in total is 10+16=26 miles.

2. Hare. The speed of the hare is constant and equal to 14 miles per hour.  But the hare stops for a two-hour nap, then the hare was 4-2=2 hours running. Then the distance that hare completed is 14·2=28 miles.

3. As you can see the hare gets farther than tortoise 2 miles.

(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