Your parentheses are in the wrong places.
But at least, unlike a large number of people who submit questions to this forum, you TRIED to use parentheses....
Here is the expression you posted: (18(x^2 - 7x + 10)/x^3 - 6x^2 + 3x + 10) =
Undoubtedly the expression you intended to show is this: 18(x^2 - 7x + 10)/(x^3 - 6x^2 + 3x + 10) =
Factor the numerator and denominator and try to simplify the expression.
The numerator factors easily....
There are many formal ways to factor the cubic polynomial in the denominator. However, since we are hoping the expression will simplify, let's check specifically to see if (x-5) and/or (x-2) are factors of the denominator.
In fact they are both factors; the expression simplifies to
The function is undefined for values that make the denominator 0: 5, 2, and -1.
In this problem, we are not concerned with where the function is undefined; we are interested in the values of x that make the expression have an integer value. So we can cancel the common factors in the numerator and denominator to simplify the expression to
That expression will have an integer value whenever (x+1) is a (positive or negative) factor of 18. We can simply make a list:
x+1 x
--------
18 17
9 8
6 5
3 2
2 1
1 0
-1 -2
-2 -3
-3 -4
-6 -7
-9 -10
-18 -19
Adding the values of x in the second column gives us a total of -12.
ANSWER: C) -12