Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?

x^2 + x + 1 + (2/ x -1)

Step-by-step explanation:

Use the divisor and find x :

x - 1 = 0  **add 1

x= 1

Now we will use the 1 in dividing:

take the coefficients from in front of all terms

  ** make sure you include 0's for x^2 and x since you have to have all terms

set it up with a 1 in a box:

1|  1   0   0  1   **bring the first number down

    1                    **multiply the boxed number by the first number and add it                                 to the second number

1|  1   0   0  1  

+1       **repeat with the rest of the terms

    1   1  

1|  1   0    0    1

 ___+1_+1_+1  

    1   1    1    2                              

**when you're done, use the new numbers to write an equation starting with a term with a degree one less than the previous equation.

**since there is a remainder, rewrite it divided by the original divisor

final

x^2 + x + 1 + (2/ x -1)

18.75 gallons

step-by-step explanation: