Question

Divide -3x3 - 4x2 + 4x +3 by x-2

Answer 1

Answer:

-3x² - 10x - 16 r. $\dfrac{-29}{x-2}$

Step-by-step explanation:

You can easily do this through synthetic division:

First step is to get all the numeric coefficients of the expression and write them down. Don't forget to bring their signs along with them.

-3x³ - 4x² + 4x +3

    | -3     -4     +4    +3

    |______________

Next we find the root that is associated with the divisor:

x  - 2 = 0

x = 2

We use this and put it outside:

 2   | -3     -4     +4    +3

      |______________

Okay now we bring down the first coefficient:

  2  | -3     -4     +4    +3

      |______________

        -3

Then we multiply it by the root and put the product under the next coefficient:

2  x - 3 = -6

2  | -3     -4     +4    +3

    |         -6                  

      -3

Then we add them:

2  | -3     -4     +4    +3

    |         -6                  

      -3    -10

Do the same steps until the end:

2  | -3     -4     +4       +3

    |         -6      -20     -32              

      -3     -10     -16     -29

Now that you have that, remember that since the divisor is in the 1st degree, quotient will have a degree will be one degree below as well.

-3x² - 10x - 26

Your last coefficient is going to be your remainder:

-3x² - 10x - 16 r. $\dfrac{-29}{x-2}$