An economist is interested in how the price of a certain item affects its sales. At a price of $p, a quantity, q, of the item is sold. If q = f(p), explain the meaning of each of the following statements: (a) f(150) = 2000 (b) f'(150) = -25

At a price of $p, a quantity, q, of the item is sold.

If q = f(p)

(a) f(150) = 2000 means at price = 150$, the number of items sold is 2000

(b) f'(150) = -25 means rate of sale is negative or the number of items sold will be decreases in future

(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