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Thread: Question on polynomials:

  1. #1
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    Question on polynomials:

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


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


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


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


    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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