( x + 1 )( x + 3 )( x + 5 )( x + 7 ) + 15
= ( x + 7 )( x + 1 )( x + 3 )( x + 5 ) + 15
= ( x" + 7x + x + 7 )( x" + 3x + 5x + 15 ) + 15
= ( x" + 8x + 11 - 4 )( x" + 8x + 11 + 4 ) + 15
= ( x" + 8x + 11 )" - 16 + 15
= ( x" + 8x + 11 + 1 )( x" + 8x + 11 - 1 )
= ( x" + 8x + 12 )( x" + 8x + 10 )
= ( x" + 2x + 6x + 12 )( x" + 8x + 4" - 16 + 10 )
= [ x( x + 2 ) + 6( x + 6 ) ][ ( x + 4 )" - 6 ]
= ( x + 2 )( x + 6 )( x + 4 + √6 )( x + 4 - √6 )
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