Question

Prove the identity: 4k^3+15k^2+17k+6=(k+1)(k+2)(4k+3) using the left side.

Answer 1

I think your best bet would be to break up some of those terms on the left side, then factor by grouping.

Working the other way, you know that the right side is equivalent to
\[(k^2+3k+2)(4k+3)\\
4k(k^2+3k+2)+3(k^2+3k+2)\\
\color{red}{4k^3+12k^2+8k+3k^2+9k+6}\]
so here's at least one way to start.