Let $a,$ $b,$ $c$ be the roots of $x^3 - 7x + 2 = 0.$  Find
\[abc + ab + ac + bc + a + b + c + 1.\]
Question:
Let $a,$ $b,$ $c$ be the roots of $x^3 - 7x + 2 = 0.$  Find
\[abc + ab + ac + bc + a + b + c + 1.\]
Answer:
Let's think step by step.

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-8
Let $a,$ $b,$ $c$ be the roots of $x^3 - 7x + 2 = 0.$  Find
\[abc + ab + ac + bc + a + b + c + 1.\]
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