Question

How do you simplify `2(k+1)^3+3(k+1)^2+k+1`?

Answer 1

`(k+1)(2k+3)(k+2)`

Explanation:

Let `k+1=x`
So `2(k+1)^3+3(k+1)^2+(k+1)`
=`2x^3+3x^2+x`
=`x(2x^2+3x+1)`
Use {cross product method}
It ca be factored as
=`x(2x+1)(x+1)`
Back!!
=`(k+1)(2k+3)(k+2)`