I am trying to factor 2 4th degree polynomials. I am stuck on both of them for different reasons.

1) I can use synthetic division and rational zero factor -3/2 to get to 2th degree. but that does not give the right quotient. multiplying the factor back it gives a different polynomial.

$\displaystyle

\begin{aligned}

6n^4+39n^3+91n^2+89n+30&=(6n^3+27n^2+37n+15)(n+2) \\

\text{divides evenly by -3/2}&=(6n^2+18n+10)(2n+3)(n+2) \\

\text{multiply factors back}&=(wrong!)(n+2)

\end{aligned}

$

2) this ones is from a book, it shows 2 solution steps from 4th degree to 2 quadratic equations? how do you do that? I tried all kinds of factoring and can't figure it out.

$\displaystyle

\begin{aligned}

2n^4+14n^3+35n^2+36n+12&=(n^2+4n+4)(2n^2+6n+3) \\

\end{aligned}

$