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The polynomial $p(x)=(ax+b)^3$ leaves a remainder of $-1$ when divided by $(x+1)$, and a remainder of $27$ when divided by $(x-2)$. Find the values of $a$ and $b$ Using the remainder theorem, I get two equations:

$b-a=-1$

$2a+b=3$

By solving this system, $a=\frac{4}{3}$ and $b=\frac{1}{3}$

Are these solutions correct? In the book the answers are $a= \frac{7}{4}$ and $b=-\frac{1}{4}$

Anne
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  • https://math.stackexchange.com/questions/1904517/whats-the-remainder-when-divided-by-x-1x-2 – lab bhattacharjee Oct 03 '17 at 18:10
  • You can check by substituting in the values of $a$ and $b$ and calculating the remainders (which are the values at $x=-1$ and $x=2$). Your answer works, the book's doesn't. – Robert Israel Oct 03 '17 at 18:15

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