Question

(x的平方+x+1)的平方-6X的平方-6x- 33 怎么因式分解?要有详细的解题过程,谢谢

Answer 1

( x" + x + 1 )" - 6x" - 6x - 33

——看到( x" + x + 1 ),就应该想到立方差

= ( x" + x + 1 )" - 6x" - 6x - 6 - 27

= ( x" + x + 1 )" - 6( x" + x + 1 ) - 27

= ( x" + x + 1 )" - 9( x" + x + 1 ) + 3( x" + x + 1 ) - 27

= ( x" + x + 1 )( x" + x + 1 - 9 ) + 3( x" + x + 1 - 9 )

= ( x" + x + 1 - 9 )( x" + x + 1 + 3 )

= ( x" + x - 8 )( x" + x + 4 )