$a)$

$8x^4+2x+3=2x+5\mid -2x-5$

$8x^4-2=0\mid :2$

$4x^4-1=0$

${\left(2x^2\right)}^2-1^2=0$

$\left(2x^2-1\right)\stackrel{\Delta =0-8<0}{\left(2x^2+1\right)}=0$

$\left(\sqrt{2}x-1\right)\left(\sqrt{2}x+1\right)\left(2x^2+1\right)=0$

$x=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\vee x=-\frac{1}{\sqrt{2}}=-\frac{\sqrt{2}}{2}$

$x=\frac{\sqrt{2}}{2}\Rightarrow y=2\cdot \frac{\sqrt{2}}{2}+5=\sqrt{2}+5\Rightarrow A=\left(\frac{\sqrt{2}}{2},\sqrt{2}+5\right)$

$x=-\frac{\sqrt{2}}{2}\Rightarrow y=2\cdot \left(-\frac{\sqrt{2}}{2}\right)+5=-\sqrt{2}+5\Rightarrow B=\left(-\frac{\sqrt{2}}{2},-\sqrt{2}+5\right)$

$b)$

$x^5-6x^3+2=-5x+2\mid +5x-2$