Giải:
\(P\left(x\right)=5x^3+2x^4-x^2+3x^2-x^3-x^4+1-4x^3\)
\(\Leftrightarrow P\left(x\right)=\left(5x^3-x^3-4x^3\right)+\left(2x^4-x^4\right)+\left(-x^2+3x^2\right)+1\)
\(\Leftrightarrow P\left(x\right)=0+x^4+2x^2+1\)
\(\Leftrightarrow P\left(x\right)=x^4+2x^2+1\)
\(\Leftrightarrow P\left(x\right)=\left(x^2+1\right)^2\)
Vì \(x^2\ge0;\forall x\)
\(\Leftrightarrow x^2+1\ge1>0;\forall x\)
\(\Leftrightarrow\left(x^2+1\right)^2>0;\forall x\)
\(\Leftrightarrow P>0;\forall x\)
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