a) \(P\left(x\right)=2x^3-2x+x^2-x^3+3x+2\)
\(=\left(2x^3-x^3\right)+x^2+\left(-2x+3x\right)+2\)
\(=x^3+x^2+x+2\)
\(Q\left(x\right)=3x^3-4x^2+3x-4x-4x^3+5x^2+1\)
\(=\left(3x^3-4x^3\right)+\left(-4x^2+5x^2\right)+\left(3x-4x\right)+1\)
\(=-x^3+x^2-x+1\)
b) \(M\left(x\right)=P\left(x\right)+Q\left(x\right)\)
\(=\left(x^3+x^2+x+2\right)+\left(-x^3+x^2-x+1\right)\)
\(=2x^2+3\)
\(N\left(x\right)=P\left(x\right)-Q\left(x\right)\)
\(=\left(x^3+x^2+x+2\right)-\left(-x^3+x^2-x+1\right)\)
\(=2x^3+2x+1\)
c) \(M\left(x\right)=2x^2+3>0\)vì \(2x^2\ge0,3>0\)do đó đa thức \(M\left(x\right)\)vô nghiệm.