At the start of a trip, a car's gas tank contains 12 gallons of gasoline. during the trip, the car consumes
gallons of gasoline. how much gasoline is left in the tank?

Step-by-step explanation:

We are given the following information in the question:

Amount of gasoline in car's tank = 12 Gallons

Let be the amount of gasoline consumed by car during the trip.

Then, we can express the amount of gasoline left in car's tank with the help of an algebraic equation.

Thus,

Example:

if x = 4 that is amount of gasoline used during trip is 4 then amount of gasoline left in car tank is

(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