a) \(P\left(x\right)=-3x^3+9-5x+7x^4-2x^2\)
\(=7x^4-3x^3-2x^2-5x+9\)
\(Q\left(x\right)=6x^2+5x-2x^4+8x^3-11\)
\(=-2x^4+8x^3+6x^2+5x-11\)
b) Ta có: \(P\left(x\right)+Q\left(x\right)\)
\(=\left(7x^4-3x^3-2x^2-5x+9\right)+\left(-2x^4+8x^3+6x^2+5x-11\right)\)
\(=7x^4-3x^3-2x^2-5x+9-2x^4+8x^{^3}+6x^2+5x-11\)
\(=\left(7x^4-2x^4\right)-\left(3x^3-8x^3\right)-\left(2x^2-6x^2\right)-\left(5x-5x\right)+\left(9-11\right)\)
\(=5x^4+5x^{^3}+4x^2 -2\)
Lại có: \(P\left(x\right)-Q\left(x\right)\)
\(=\left(7x^4-3x^3-2x^2-5x+9\right)-\left(-2x^4+8x^3+6x^2+5x-11\right)\)
\(=7x^4-3x^3-2x^2-5x+9+2x^4-8x^3-6x^2-5x+11\)
\(=\left(7x^4+2x^4\right)-\left(3x^3+8x^3\right)-\left(2x^2+6x^2\right)-\left(5x+5x\right)+\left(9+11\right)\)
\(=9x^4-11x^3-8x^2-10x+20\)
