a.
\(f\left(x\right)=-\left(x^4-2x^2+1\right)-3\left(x-1\right)+3=-\left(x-1\right)^2\left(x+1\right)^2-3\left(x-1\right)+3\)
\(f\left(x\right)⋮x-1\Rightarrow3⋮x-1\)
\(\Rightarrow x-1=Ư\left(3\right)=\left\{-3;-1;1;3\right\}\)
\(\Rightarrow x=\left\{-2;0;2;4\right\}\)
Mà x nguyên âm \(\Rightarrow x=-2\)
b.
\(B=\left(x^2+y^2+4-2xy+4x-4y\right)+4y^2-2024\)
\(=\left(x-y+2\right)^2+4y^2-2024\ge-2024\)
\(B_{min}=-2024\) khi \(\left(x;y\right)=\left(-2;0\right)\)
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