a/ \(P\left(x\right)=5x^4+3x^3+4x^2-3x+1\)
\(Q\left(x\right)=7x^4-x^3-3x^2-5\)
b/ \(P\left(x\right)+Q\left(x\right)=5x^4+3x^3+4x^2-3x+1+7x^4-x^3-3x^2-5=12x^4+2x^3+x^2-3x-4\)
\(P\left(x\right)-Q\left(x\right)=5x^4+3x^3+4x^2-3x+1-\left(7x^4-x^3-3x^2-5\right)=5x^4+3x^3+4x^2-3x+1-7x^4+x^3+3x^2+5=-2x^4+4x^3+7x^2-3x+6\)