Rearrange polynomial: -4k^2x^3+x^2+2x+2k+3
Use the Remainder Theorem (Factor Theorem): if r is a root of f(x), that is x-r is a factor of f(x), then f(r)=0, where r=-2k:
-4k^2(-2k)^3+(-2k)^2+2(-2k)+2k+3=0;
32k^5+4k^2-4k+2k+3=32k^5+4k^2-2k+3=0; from this k=-0.7289 approx.
(The polynomial in k was solved using a calculator and an iterative process.)
f(x)=x^2-2.1250x^3+2x+1.5423, and the factor is x-1.4577.