(x^2+10x+26)/(x+6) how do you get the quotient and remainder

quotient is x+4 and remainder 2.

Step-by-step explanation:

Given an polynomial of degree 2 and we are to divide it by x+6.

To find quotient and remainder

We can do synthetic division

When we divide by x+6 consider -6

and write on left.  Write the coefficient 1 , 10, 26 inside

-6       1      10     26

         x       -6    -24

       ---------------------

          1      4       2 =R

So remainder is 2 and quotient is x+4

Let us verify

(x+4)(x+6) =

If we add the remainder we are getting the given expression.