因式分解的题目

来源：百度知道 编辑：UC知道 时间：2024/05/13 10:26:47
第一题：X四次-6X两次-7X-6
二 X四次-10X三次+35X二次-48X+18

第一题
原式=x^2(x^2-4)-2x^2-7x-6
=x^2(x+2)(x-2)-(2x+3)(x+2)
=(x+2)[x^2(x-2)-(2x+3)]
=(x+2)(x^3-2x^2-2x-3)
=(x+2)[x^2(x-3)+x^2-2x-3]
=(x+2)[x^2(x-3)+(x+1)(x-3)]
=(x+2)(x-3)(x^2+x+1)

第二题
原式=x^2(x^2-10x+21)+(14x^2-48x+18)
=x^2(x-3)(x-7)+2(7x-3)(x-3)
=(x-3)(x^3-7x^2+14x-6)
=(x-3)[x^2(x-3)-4x^2-14x+6]
=[x-3][x^2(x-3)-(2x-1)(2x-6)]
=[x-3]^2[x^2-4x+2]

x^4-6x^2-7x-6
=x^4-4x^2-[2x^2+7x+6]
=x^2[x^2-4]-[2x+3][x+2]
=x^2[x+2][x-2]-[2x+3][x+2]
=[x+2][x^3-2x^2-2x-3]
=[x+2][x^2(x-3)+(x^2-2x-3)]
=[x+2][x^2(x-3)+(x-3)(x+1)]
=[x+2][x-3][x^2+x+1]

x^4-10x^3+35x^2-48x+18
=x^2[x^2-10x+21]+[14x^2-48x+18]
=x^2[x-3][x-7]+2[7x-3][x-3]
=[x-3][x^3-7x^2+14x-6]
=[x-3][x^2[x-3]-[4x^2-14x+6]
=[x-3][x^2(x-3)-(2x-1)(2x-6)]
=[x-3]^2[x^2-4x+2]

第一题(x+2)(x-3)(X二次+x+1)
二 (x-3)(x-3)(X二次-4x+2)