\(a,H\left(x\right)=2x^2+11x+5=0\\ \Leftrightarrow\left(2x^2+10x\right)+\left(x+5\right)=0\\ \Leftrightarrow2x\left(x+5\right)+\left(x+5\right)=0\\ \Leftrightarrow\left(x+5\right)\left(2x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-5\\x=-\dfrac{1}{2}\end{matrix}\right.\\ b,K\left(x\right)=5x^2-8x-4=0\\ \Leftrightarrow\left(5x^2-10x\right)+\left(2x-4\right)=0\\ \Leftrightarrow5x\left(x-2\right)+2\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(5x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{2}{5}\end{matrix}\right.\)
\(c,Q\left(x\right)=4x^2+8x+3=0\\ \Leftrightarrow\left(4x^2+2x\right)+\left(6x+3\right)=0\\ \Leftrightarrow2x\left(2x+1\right)+3\left(2x+1\right)=0\\ \Leftrightarrow\left(2x+1\right)\left(2x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\\ d,P\left(x\right)=x^3+x^2+x+1=0\\ \Leftrightarrow x^2\left(x+1\right)+\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2=-1\left(ktm\right)\end{matrix}\right.\)