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Math Help - remainder theorem

  1. #1
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    remainder theorem

    The expressions x^3-7x+6 and x^3-x^2-4x+24 have the same remainder when divided by (x+p)

    Find the possible values of p.

    what i did

     <br />
-p^3-7(-p)+6=(-p^3)-(-p)^2-4(-p)+24<br />
     <br />
-p^3+7p+6=-p^3-p^2+4p+24<br />
     <br />
-p^3+7p+6-[-p^3-p^2+4p+24]=0<br />
     <br />
p^2+3p-18=0<br />
     <br />
p=3,-6<br />

    however, ans is 3,-3!!
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  2. #2
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    Hello, Punch!

    Absolutely correct . . . good work!
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Punch View Post
    The expressions x^3-7x+6 and x^3-x^2-4x+24 have the same remainder when divided by (x+p)

    Find the possible values of p.

    what i did

     <br />
-p^3-7(-p)+6=(-p^3)-(-p)^2-4(-p)+24<br />
     <br />
-p^3+7p+6=-p^3-p^2+4p+24<br />
     <br />
-p^3+7p+6-[-p^3-p^2+4p+24]=0<br />
     <br />
p^2+3p-18=0<br />
     <br />
p=3,-6<br />

    however, ans is 3,-3!!

    It comes out that 3 and -6 are indeed the correct answers.

    when you divide the given terms by (x+3), the remainder is 0 in both the cases.

    when you divide the given terms by (x-6), you remainder in both the cases is 180

    But if you divide the given terms by (x-3), the remainders are not the same..

    You can check back by dividing the terms by (x+3), (x-6), and (x-3), and you'll see 3 and -6 are the correct values for p...
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  4. #4
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    Thanks!! I was confused about why my answer was different from the answer sheet!!! i repeated the question 5 times
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