Answer:
-3x² - 10x - 16 r. [tex]\dfrac{-29}{x-2}[/tex]
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. [tex]\dfrac{-29}{x-2}[/tex]
