Đáp án đúng: C
Giải chi tiết:\(\begin{array}{l}\,f\left( x \right) = 5{x^5} - 3x - 6{x^4} + 2{x^3} + 6 + 4{x^2}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5{x^5} - 6{x^4} + 2{x^3} + 4{x^2} - 3x + 6\\g\left( x \right) = - 2{x^4} - x + 4{x^2} + 5 - 5{x^5} + 2{x^3}\\\,\,\,\,\,\,\,\,\,\,\,\, = \, - 5{x^5} - 2{x^4} + 2{x^3} + 4{x^2} - x + 5\\ \Rightarrow f\left( x \right) + g\left( x \right) = 5{x^5} - 6{x^4} + 2{x^3} + 4{x^2} - 3x + 6 + \left( { - 5{x^5} - 2{x^4} + 2{x^3} + 4{x^2} - x + 5} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,\left( {5{x^5} - 5{x^5}} \right) + \left( { - 6{x^4} - 2{x^4}} \right) + \left( {2{x^3} + 2{x^3}} \right) + \left( {4{x^2} + 4{x^2}} \right) + \left( { - 3x - x} \right) + \left( {6 + 5} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,\, - 8{x^4} + 4{x^3} + 8{x^2} - 4x + 11\\f\left( x \right) - g\left( x \right) = 5{x^5} - 6{x^4} + 2{x^3} + 4{x^2} - 3x + 6 - \left( { - 5{x^5} - 2{x^4} + 2{x^3} + 4{x^2} - x + 5} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,5{x^5} - 6{x^4} + 2{x^3} + 4{x^2} - 3x + 6 + 5{x^5} + 2{x^4} - 2{x^3} - 4{x^2} + x - 5\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,\left( {5{x^5} + 5{x^5}} \right) + \left( { - 6{x^4} + 2{x^4}} \right) + \left( {2{x^3} - 2{x^3}} \right) + \left( {4{x^2} - 4{x^2}} \right) + \left( { - 3x + x} \right) + \left( {6 - 5} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,10{x^5} - 4{x^4} - 2x + 1\end{array}\)
Vậy \(f\left( x \right) + g\left( x \right) = - 8{x^4} + 4{x^3} + 8{x^2} - 4x + 11;\,\,\,f\left( x \right) - g\left( x \right) = 10{x^5} - 4{x^4} - 2x + 1\)
Bậc của \(f\left( x \right) + g\left( x \right)\) là 4.
Bậc của \(f\left( x \right) - g\left( x \right)\) là 5.
Chọn C