So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:
(Note that synthetic division can only be used when the divisor is a 1st degree binomial)
Now firstly, drop the 1:
Next, you are going to multiply -10 and 1, and then combine the product with 2.
Next, multiply -10 and -8, then combine the product with -82:
Next, multiply -10 and -2, then combine the product with -28:
Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).
Putting it together, the quotient is [tex]k^2-8k-2-\frac{8}{k+10}[/tex]
