`a) f( x ) = x^5 - 3x^2 + 7x^4 - 9x^3 - 1/4 x`

            `= x^5 + 7x^4 - 9x^3 - 3x^2 - 1/4x`

    `g( x ) = 5x^4 - x^5 + x^2 + 3x^2 - 1/4`

             `= - x^5 + 5x^4 + ( x^2 + 3x^2 ) - 1/4`

             `= - x^5 + 5x^4 + 4x^2 - 1/4`

`b) f( x ) + g( x ) = ( x^5 + 7x^4 - 9x^3 - 3x^2 - 1/4 x ) + ( - x^5 + 5x^4 + 4x^2 - 1/4 )`

`= x^5 + 7x^4 - 9x^3 - 3x^2 - 1/4x - x^5 + 5x^4 + 4x^2 - 1/4`

`= ( x^5 - x^5 ) + ( 7x^4 + 5x^4 ) + ( - 9x^3 ) + ( - 3x^2 + 4x^2 ) + ( - 1/4x ) + ( - 1/4 )`

`= 12x^4 - 9x^3 + x^2 - 1/4x - 1/4`

$\\$

`f( x ) - g( x ) = ( x^5 + 7x^4 - 9x^3 - 3x^2 - 1/4 x ) - ( - x^5 + 5x^4 + 4x^2 - 1/4 )`

`= x^5 + 7x^4 - 9x^3 - 3x^2 - 1/4x + x^5 - 5x^4 - 4x^2 + 1/4`

`= ( x^5 + x^5 ) + ( 7x^4 - 5x^4 ) + ( - 9x^3 ) + ( - 3x^2 - 4x^2 ) + ( - 1/4 x ) + 1/4`

`= 2x^5 + 2x^4 - 9x^3 - 7x^2 - 1/4x + 1/4`

Đáp án:`+`Giải thích các bước giải:

`a)`

`f(x)=x^5-3x^2+7x^4-9x^3-1/4x`

`=x^5+7x^4-9x^3-3x^2-1/4x`

`g(x)=5x^4-x^5+x^2+3x^2-1/4`

`=-x^5+5x^4+(x^2+3x^2)-1/4`

`=-x^5+5x^4+4x^2-1/4`

`b)`

`f(x)+g(x)`

`=(x^5+7x^4-9x^3-3x^2-1/4x)+(-x^5+5x^4+4x^2-1/4)`

`=x^5+7x^4-9x^3-3x^2-1/4x-x^5+5x^4+4x^2-1/4`

`=(x^5-x^5)+(7x^4+5x^4)-9x^3+(-3x^2+4x^2)-1/4x-1/4` 

`=12x^4-9x^3+x^2-1/4x-1/4`

`f(x)-g(x)`

`=(x^5+7x^4-9x^3-3x^2-1/4x)-(-x^5+5x^4+4x^2-1/4)`

`=x^5+7x^4-9x^3-3x^2-1/4x+x^5-5x^4-4x^2+1/4`

`=(x^5+x^5)+(7x^4-5x^4)-9x^3+(-3x^2-4x^2)-1/4x+1/4`

`=2x^5+2x^4-9x^3-7x^2-1/4x+1/4`