To prove that x= 1 is the solution of the original equation, it is actually required that one root of the equation is 1, that is, x= 1.

For the problem of finding the roots of quadratic or above equations, the factorization method is considered first.

Put x= 1 directly into the original equation, and left = right = 0, and prove it.

But I use factorization to prove:

Now factorize the equation x 3-(2m+1)+(3m+2)-m-2 = 0:

The original types are arranged as follows:

x^3+(3m+3- 1)x-(2m+ 1-(m+2)=0.

x^3-x+(3m+3)x-(3m+3)=0.

x(x^2- 1)+(3m+3)(x- 1)=0.

x(x+ 1)(x- 1)+(3m+3)(x- 1)= 0。

(x- 1)[x(x+ 1)+3m+3]= 0。

x- 1=0，

x= 1。

∴x= 1 is the root of the original equation,

Complete the certificate.

2.∫(x- 1)[x(x+ 1)+3m+3)= 0。 It can be broken down into:

∴x^3-(2m+ 1)+(3m+2)x-m-2=(x- 1)(x^2+x+3m+3)