Đáp án + Giải thích các bước giải:
`a)`
`f(x)=-3x^{2}+x-1+x^{4}-x^{3}-x^{2}+3x^{4}`
`=(x^{4}+3x^{4})-x^{3}-(3x^{2}+x^{2})+x-1`
`=4x^{4}-x^{3}-4x^{2}+x-1`
``
`g(x)=x^{4}+x^{2}-x^{3}+x-5+5x^{3}-x^{2}`
`=x^{4}+(5x^{3}-x^{3})+(x^{2}-x^{2})+x-5`
`=x^{4}+4x^{3}+x-5`
`b)`
`f(x)-g(x)=4x^{4}-x^{3}-4x^{2}+x-1-(x^{4}+4x^{3}+x-5)`
`=4x^{4}-x^{3}-4x^{2}+x-1-x^{4}-4x^{3}-x+5`
`=(4x^{4}-x^{4})-(x^{3}+4x^{3})-4x^{2}+(x-x)+(5-1)`
`=3x^{4}-5x^{3}-4x^{2}+4`
``
`f(x)+g(x)= 4x^{4}-x^{3}-4x^{2}+x-1+x^{4}+4x^{3}+x-5`
`=(4x^{4}+x^{4})+(4x^{3}-x^{3})-4x^{2}+(x+x)-(5+1)`
`=5x^{4}+3x^{3}-4x^{2}+2x-6`
`c)`
`g(-1)=(-1)^{4}+4.(-1)^{3}+(-1)-5`
`=1-4-1-5`
`=-9`