What is the result of dividing 2x^3+x^2−2x+8 by x + 2

The answer is 2x² - 3x +4

Step-by-step explanation:

2x³+x²-2x+8 / x+2

= (x+2) (2x²-3x+4) / x+2

eliminate x+2

= 2x² - 3x +4

So for this, I will be using synthetic division. To set this up, take the root of the divisor (x + 2) and put it on one end, and then take the coefficients of the dividend (2x³ + x² - 2x + 8) and put it on the other end.

Now our division is set up. Firstly, drop the 2:

Next, multiply -2 and 2, then add the product with 1:

Next, multiply -2 and -3, then add the product with -2:

Next, multiply 4 and -2, then add the product with 8:

Now, we have just solved for the coefficients and constants. Since the dividend has a degree of 3, this means that our quotient has a degree of 2. With this info, this makes our final 2x² - 3x + 4