(a) Find all roots of $(x^2+4*x+3)$ in $\mathbb{Z}_{20} [x]$.


(b) Find all factorizations of $(x^2+4*x+3)$ of the form $( x - A )( x - B )$ in the ring $\mathbb{Z}_{20} [x]$. There may be fewer than 5 distinct factorizations; enter your factorization(s) from the top row down, and leave blank row(s) below if you don't use all 5.

$(x^2+4*x+3) = ($ $)($ $)$
$\phantom{ (x^2+4*x+3) } = ($ $)($ $)$
$\phantom{ (x^2+4*x+3) } = ($ $)($ $)$
$\phantom{ (x^2+4*x+3) } = ($ $)($ $)$
$\phantom{ (x^2+4*x+3) } = ($ $)($ $)$