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Math Help - Algebra problem

  1. #1
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    Algebra problem

    I would appreciate if you can solve this problem. thanks.


    What is the greatest integer value of x such that (X^2 + 2X + 5)/(x - 3) is an integer?
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  2. #2
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    Quote Originally Posted by chil2e View Post
    I would appreciate if you can solve this problem. thanks.


    What is the greatest integer value of x such that (X^2 + 2X + 5)/(x - 3) is an integer?
    hmmmm ok so lets see if i got this right...
    In order for (X^2 + 2X + 5)/(x - 3) to be an interger, that means when you do the long division, there is no remainder. Now if you actually try doing the long division of polynomials (here I am assuming you know how to divide polynomials) you are going to notice that there is a remainder of 20/(x-3) now in order for it to be an integer answer, the remainder has to be an integer. The highest number that x can be that would make the remainder an integer would be 23. I think this should work...
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  3. #3
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    As \frac{x^2 + 2x + 5}{x - 3} = x+5 +\frac{20}{x-3} <br />

    Then by inspection  x+5 +\frac{20}{x-3} the first part of the expression x+5 will always give an integer for any integer x so we just have use the same idea to inspect  \frac{20}{x-3}

    As we are looking for an integer there are only so many numbers that will work, I can think of x = 13,23
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