因式分解(x^5+x^4+5x^2+5x+6)/(x^2+x+1)

题目

因式分解(x^5+x^4+5x^2+5x+6)/(x^2+x+1)

答案

( x^5 + x^4 + 5x" + 5x + 6 ) / ( x" + x + 1 )
先想想,怎样约分,去分母
= ( x^5 + x^4 + x"' - x"' - x" - x + 6x" + 6x + 6 ) / ( x" + x + 1 )
= [ x"'( x" + x + 1 ) - x( x" + x + 1 ) + 6( x" + x + 1 ) ] / ( x" + x + 1 )
= ( x" + x + 1 )( x"' - x + 6 ) / ( x" + x + 1 )
= x"' - x + 6
下面还是用立方和、立方差分解
= x"' + 8 - x - 2
= ( x"' + 2"' ) - ( x + 2 )
= ( x + 2 )( x" - 2x + 4 ) - ( x + 2 )
= ( x + 2 )( x" - 2x + 3 )