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Math Help - Question on polynomials:

  1. #1
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    Question on polynomials:

    If P(x) has remainder 2 when divided by (x-3) and remainder -13 when divided by (x+2), find the remainder when P(x) is divided by (x^2 - x - 6)


    I know that P(k)=Q(k)(k-k)+R =R


    Please, I need help for this one!
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  2. #2
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    Quote Originally Posted by karldiesen View Post
    If P(x) has remainder 2 when divided by (x-3) and remainder -13 when divided by (x+2), find the remainder when P(x) is divided by (x^2 - x - 6)


    I know that P(k)=Q(k)(k-k)+R =R


    Please, I need help for this one!
    So you know that P(x)= (x-3)Q(x)+ 2= (x+2)R(x)- 13. Then (x+2)P(x)= (x+2)(x-3)Q(x)+ 2(x+2) and (x-3)P(x)= (x+2)(x-3)R(x)- 13(x- 3). Subtracting the two equations, ((x+2)- (x- 3))P(x)= 5P(x)= (x+2)(x-3)(Q(x)- R(x))+ 15x- 35. P(x)= (x+2)(x-3)S(x)+ 3x- 7 where S(x) is (Q(x)- R(x))/5.
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