a) \(P\left(x\right)=3x^3+2x^2-2x+7-x^2-x\)
\(P\left(x\right)=3x^3+\left(2x^2-x^2\right)+\left(-2x-x\right)+7\\ P\left(x\right)=3x^3+x^2-3x+7\)
\(Q\left(x\right)=-3x^3+x-14-2x-x^2-1\\ Q\left(x\right)=-3x^3-x^2+\left(x-2x\right)+\left(-14-1\right)\\ Q\left(x\right)=-3x^3-x^2-x-15\)
b) Ta có:
\(M\left(x\right)=P\left(x\right)+Q\left(x\right)\\ M\left(x\right)=\left(3x^3-3x^3\right)+\left(x^2-x^2\right)+\left(-3x-x\right)+\left(7-15\right)\\ M\left(x\right)=-4x-8\)
\(N\left(x\right)=P\left(x\right)-Q\left(x\right)\\ N\left(x\right)=3x^3+x^2-3x+7+3x^3+x^2+x+15\\ N\left(x\right)=\left(3x^3+3x^3\right)+\left(x^2+x^2\right)+\left(-3x+x\right)+\left(7+15\right)\\ N\left(x\right)=6x^3+2x^2-2x+22\)
c) \(P\left(x\right)=-Q\left(x\right)\)
\(3x^3+x^2-3x+7=-\left(-3x^3-x^2-x-15\right)\\ 3x^3+x^2-3x+7=3x^3+x^2+x+15\\ -4x=8\\ x=-2\)
