Question 1189444
<br>
Your parentheses are in the wrong places.<br>
But at least, unlike a large number of people who submit questions to this forum, you TRIED to use parentheses....<br>
Here is the expression you posted: (18(x^2 - 7x + 10)/x^3 - 6x^2 + 3x + 10) = {{{(18(x^2 - 7x + 10)/x^3 - 6x^2 + 3x + 10)}}}<br>
Undoubtedly the expression you intended to show is this: 18(x^2 - 7x + 10)/(x^3 - 6x^2 + 3x + 10) = {{{18(x^2 - 7x + 10)/(x^3 - 6x^2 + 3x + 10)}}}<br>
Factor the numerator and denominator and try to simplify the expression.<br>
The numerator factors easily....<br>
{{{18((x-5)(x-2))/(x^3 - 6x^2 + 3x + 10)}}}<br>
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.<br>
In fact they are both factors; the expression simplifies to<br>
{{{18((x-5)(x-2))/((x-5)(x-2)(x+1))}}}<br>
The function is undefined for values that make the denominator 0: 5, 2, and -1.<br>
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<br>
{{{18/(x+1)}}}<br>
That expression will have an integer value whenever (x+1) is a (positive or negative) factor of 18.  We can simply make a list:<br><pre>
   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</pre>
Adding the values of x in the second column gives us a total of -12.<br>
ANSWER: C) -12<br>