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A factored polynomial reveals its roots, a key concept in understanding the behavior of these expressions.

Find the sum of all real solutions of the equation \[x^3+x^2 + x=8x^2+8 x + 8.\]

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The polynomial in two variables

\[ f(x,y) = xy + 3y - 4x -12 \]

can be expressed as the product of two linear factors with integer coefficients, namely

\[ f(x,y) = (ax + by + c) ( dx + ey + f). \]

Evaluate \( |a+b+c| + |d+e+f| \).

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