2 x + 2 ⋅ x 2 + 6 x + 8 4 x + 20 = 2 x + 2 ⋅ x 2 + 2 x + 4 x + 8 2 ( 2 x + 10 ) = ( x + 2 ) ⋅ x ( x + 2 ) + 4 ( x + 2 ) 2 x + 10 = ( x + 2 ) ⋅ ( x + 4 ) ( x + 2 ) 2 x + 10 = x + 4 2 x + 10
2 x + 2 ⋅ x 2 + 6 x + 8 4 x + 20 x 2 + 6 x + 8 = 0 x 2 + 4 x + 2 x + 8 = 0 x ( x + 4 ) + 2 ( x + 4 ) = 0 ( x + 4 ) ( x + 2 ) = 0
x + 4 = 0 ∧ x + 2 = 0 x = − 4 ∧ x = − 2 D = R ∖ { − 4 , − 2 }
2 x + 2 ⋅ x 2 + 6 x + 8 4 x + 20 = 2 1 ( x + 2 ) 1 ⋅ ( x + 2 ) 1 ( x + 4 ) 4 2 ( x + 5 ) = x + 4 2 ( x + 5 )
The expression 2 x + 2 ⋅ x 2 + 6 x + 8 4 x + 20 simplifies to x + 4 2 ( x + 5 ) after factoring and canceling common terms. This makes it easier to handle the algebraic expression in a more manageable form. By carefully working through each step, we achieve a clear and precise final result.
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