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x^2 + 6x+8 = x^2 + 4x +2x +8
= x( x+4) +2( x+4)
= ( x+2)( x+4)
( x^2 + 5x +6) = x^2 + 2x+ 3x +6
= x( x+2) +3( x+2)
= ( x+3)( x+2)
( x^2 + 7x +12)
x^2 +4x +3x +12
x( x+4)+3(x+4)
( x+3)( x+4)
So
( x^2 + 6x +8)( x^2 +5x+6)( x^2 + 7x +12)
( x+2)( x+4)( x+3)( x+2)( x+3)( x+4)
( x+2)^2 ( x+4)^2 ( x+3)^2
square root of it is
( x+2)( x+4)( x+3)
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