Q10Digital Electronics

We must mathematically expand the algebraic equation $(23{)}_x+(12{)}_x=(101{)}_x$ strictly into its constituent polynomial terms based on powers of the unknown radix $x$. This yields: $(2x^1+3x^0)+(1x^1+2x^0)=(1x^2+0x^1+1x^0)$. Simplifying: $2x+3+x+2=x^2+1$. Thus, $3x+5=x^2+1$, which algebraically rearranges to the quadratic equation $x^2-3x-4=0$. Factoring yields $(x-4)(x+1)=0$. Since a number base physically cannot be negative, $x=4$.