Foiled once again

Algebra Level 2

The polynomial in two variables

f(x,y)=xy+3y4x12 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). f(x,y) = (ax + by + c) ( dx + ey + f).

Evaluate a+b+c+d+e+f |a+b+c| + |d+e+f| .

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