a, \(P\left(x\right)=x^4+3x^3+x^2+2x+2\)
\(Q\left(x\right)=x^4+x^3+2x^2+2x+1\)
b, \(P\left(x\right)+Q\left(x\right)=x^4+3x^3+x^2+2x+2+x^4+x^3+2x^2+2x+2\\ =2x^4+4x^3+3x^2+4x+4\)
\(P\left(x\right)-Q\left(x\right)=x^4+3x^3+x^2+2x+2-x^4-x^3-2x^2-2x-1=2x^3-x^2+1\)
a: \(P\left(x\right)=2x^4+3x^3+3x^2-x^4-4x+2-2x^2+6x\)
\(=\left(2x^4-x^4\right)+3x^3+\left(3x^2-2x^2\right)+\left(-4x+6x\right)+2\)
\(=x^4+3x^3+x^2+2x+2\)
\(Q\left(x\right)=x^4+3x^2+5x-1-x^2-3x+2+x^3\)
\(=x^4+x^3+\left(3x^2-x^2\right)+\left(5x-3x\right)+2-1\)
\(=x^4+x^3+2x^2+2x+1\)
b: P(x)+Q(x)
\(=x^4+3x^3+x^2+2x+2+x^4+x^3+2x^2+2x+1\)
\(=2x^4+4x^3+3x^2+4x+3\)
P(x)-Q(x)
\(=x^4+3x^3+x^2+2x+2-x^4-x^3-2x^2-2x-1\)
\(=2x^3-x^2+1\)
a) \(P\left(x\right)=2x^4+3x^3+3x^2-x^4-4x+2-2x^2+6x=\left(2x^4-x^4\right)+3x^3+\left(3x^2-2x^2\right)+\left(-4x+6x\right)+2=x^4+3x^3+x^2+2x+2\)\(Q\left(x\right)=x^4+3x^2+5x-1-x^2-3x+2+x^3=x^4+x^3+\left(3x^2-x^2\right)+\left(5x-3x\right)+\left(-1+2\right)=x^4+x^3+2x^2+2x+1\)
b) \(P\left(x\right)+Q\left(x\right)=x^4+3x^3+x^2+2x+2+x^4+x^3+2x^2+2x+1=\left(x^4+x^4\right)+\left(3x^3+x^3\right)+\left(x^2+2x^2\right)+\left(2x+2x\right)+\left(2+1\right)=2x^4+4x^3+3x^2+4x+3\)
\(P\left(x\right)-Q\left(x\right)=x^4+3x^3+x^2+2x+2-\left(x^4+x^3+2x^2+2x+1\right)=x^4^{ }+3x^3+x^2+2x+2-x^4-x^3-2x^2-2x-1=\left(x^4-x^4\right)+\left(3x^3-x^3\right)+\left(x^2-2x^2\right)+\left(2x-2x\right)+\left(2-1\right)=2x^3+x^2+1\)
