Question

因式分解(x²-5x+8)(x²-5x+2)+8

Answer 1

( x" - 5x + 8 )( x" - 5x + 2 ) + 8
= ( x" - 5x )" + 10( x" - 5x ) + 16 + 8
= ( x" - 5x )" + 4( x" - 5x ) + 6( x" - 5x ) + 24
= ( x" - 5x )( x" - 5x + 4 ) + 6( x" - 5x + 4 )
= ( x" - 5x + 4 )( x" - 5x + 6 )

= ( x" - x - 4x + 4 )( x" - 2x - 3x + 6 )
= [ x( x - 1 ) - 4( x - 1 ) ][ x( x - 2 ) - 3( x - 2 ) ]
= ( x - 4 )( x - 1 )( x - 2 )( x - 3 )
= ( x - 1 )( x - 2 )( x - 3 )( x - 4 )