A gardener is planting two types of trees: Type A is 3 feet tall and grows at a rate of 23 inches per year. Type B is 6 feet tall and grows at a rate of 17 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

it will take 0.5 year for these trees to be the same height.

Step-by-step explanation:

Let x represent the number of years it will take for these trees to be the same height.

Type A is 3 feet tall and grows at a rate of 23 inches per year. It means that the height of Type A after x years is

23x + 3

Type B is 6 feet tall and grows at a rate of 17 inches per year. It means that the height of Type B after x years is

17x + 6

For the height of both trees to be the same, the number of years would be

23x + 3 = 17x + 6

23x - 17x = 6 - 3

6x = 3

x = 3/6

x = 0.5

(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