Math

[Guest]

Prove that if a,b,c are positive integers then
a+b+c-1 is a factor of
a²b+c²b+2abc-b³-2b²-b.

[shyamjayakannan]

[tex]a^2b+c^2b+2abc-b^3-2b^2-b=b\left(a^2+c^2+2ac-b^2-2b-1\right)=b\left\{(a+c)^2-(b+1)^2\right\}[/tex]
[tex]=b(a+c+b+1)(a+c-b-1)[/tex]