Question

因式分解5x^6-7x^5-8x^4-x^3+7x^2+8x-4？

Answer 1

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 ),1,六个零点:
2.0000
-1.0000
-0.5000 + 0.8660i
-0.5000 - 0.8660i
1.0000
0.4000
系数：5
则分解为5*(x-2)(x+1)(x-1)(x-0.4)(x+0.5-0.886i)(x+0.5+0.886i)=(x-2)(x+1)(x-1)(5x-2)(x^2+x+1),1,