Question

因式分解5x^6-7x^5-8x^4-x^3+7x^2+8x-4..

Answer 1

Answer 2

5(x^6) - 7(x^5) - 8(x^4) - x"' + 7x" + 8x - 4
= 4(x^6) - 4 + x^6 - x"' - 7(x^5) + 7x" - 8(x^4) + 8x
= 4( x^6 - 1 ) + x"'( x"' - 1 ) - 7x"( x"' - 1 ) - 8x( x"' - 1 )
= 4( x"' + 1 )( x"' - 1 ) + x( x" - 7x - 8 )( x"' - 1 )
= 4( x + 1 )( x" - x + 1 )( 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 )

Answer 3

(x-1)*(x-2)*(5*x-2)*(x+1)*(x^2+x+1)