You can 
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(n³ + 9n² - 7n + 23)÷(n + 10)
                n²  -   n +  3
n + 10)  n³ +  9n²  -  7n + 23
       -(n³ + 10n²)
               -n²  -  7n
             -(-n²  - 10n)
                       3n + 23
                     -(3n + 30)
                            -7
Answer:  n² - n + 3 + 
or
         n² - n + 3 - 
or you can do it by synthetic division:
-10|1   9  -7   23
   |  -10  10  -30
    1  -1   3   -7 
Same answer.
Edwin