# Finding the values of $a$ and $b$ in polynomial $p(x)$ knowing the remainders of two divisors

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 $b=-\frac{1}{4}$