<s>[INST] Suppose $a, b, c \in I$ such that greatest common divisor of $x^2 + ax + b$ and $x^2 + bx + c$ is $(x + 1)$ and the least common multiple... 
Suppose $a, b, c \in I$ such that greatest common divisor of $x^2 + ax + b$ and $x^2 + bx + c$ is $(x + 1)$ and the least common multiple of $x^2 + ax + b$ and $x^2 + bx + c$ is $(x^3 - 4x^2 + x + 6)$. Find the value of $|a + b + c|$.

My attempt : 
$$x^2 + ax + b = (x + 1)Y$$
$$x^2 + bx + c = (x + 1)Z$$
From here onwards I do not how to continue. Please help. Thank you!
 [/INST] Using GCD $\times$ LCM = Product, we get
$$(x+1)(x^3 - 4x^2 + x + 6) = (x^2+ax+b)(x^2+bx+c)$$
Now it remains to equate coefficients on both sides to get $(a, b, c) = (-1, -2, -3)$
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