神马作文网因式分解5x^6-7x^5-8x^4-x^3+7x^2+8x-4
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/09/21 13:38:32
因式分解5x^6-7x^5-8x^4-x^3+7x^2+8x-4
5(x^6) - 7(x^5) - 8(x^4) - x"' + 7x" + 8x - 4
= 4(x^6) + x^6 - 7(x^5) - 8(x^4) - x"' + 7x" + 8x - 4
= 4( x^6 - 1 ) + (x^4)( x" - 7x - 8 ) - x( x" - 7x - 8 )
= 4( x"' - 1 )( x"' + 1 ) + x( x"' - 1 )( x" - 7x - 8 )
= 4( x"' - 1 )( x + 1 )( x" - x + 1 ) + x( x - 8x + x - 8 )( x"' - 1 )
= 4( x"' - 1 )( x + 1 )( x" - x + 1 ) + x( x - 8 )( x + 1 )( x"' - 1 )
= ( x + 1 )( x"' - 1 )( 4x" - 4x + 4 + x" - 8x )
= ( x + 1 )( x - 1 )( x" + x + 1 )( 5x" - 12x + 4 )
= ( x - 1 )( x + 1 )( x" + x + 1 )( 5x" - 10x - 2x + 4 )
= ( x - 1 )( x + 1 )( x - 2 )( 5x - 2 )( x" + x + 1 )
= 4(x^6) + x^6 - 7(x^5) - 8(x^4) - x"' + 7x" + 8x - 4
= 4( x^6 - 1 ) + (x^4)( x" - 7x - 8 ) - x( x" - 7x - 8 )
= 4( x"' - 1 )( x"' + 1 ) + x( x"' - 1 )( x" - 7x - 8 )
= 4( x"' - 1 )( x + 1 )( x" - x + 1 ) + x( x - 8x + x - 8 )( x"' - 1 )
= 4( x"' - 1 )( x + 1 )( x" - x + 1 ) + x( x - 8 )( x + 1 )( x"' - 1 )
= ( x + 1 )( x"' - 1 )( 4x" - 4x + 4 + x" - 8x )
= ( x + 1 )( x - 1 )( x" + x + 1 )( 5x" - 12x + 4 )
= ( x - 1 )( x + 1 )( x" + x + 1 )( 5x" - 10x - 2x + 4 )
= ( x - 1 )( x + 1 )( x - 2 )( 5x - 2 )( x" + x + 1 )
因式分解5x^6-7x^5-8x^4-x^3+7x^2+8x-4
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