Đáp án + Giải thích các bước giải:
`a//`
`P(x)=-3x^{2}+3x^{4}+5x^{3}+x^{2}-x-2`
`=3x^{4}+5x^{3}+(x^{2}-3x^{2})-x-2`
`=3x^{4}+5x^{3}-2x^{2}-x-2`
`--------`
`Q(x)=-2x^{4}+x^{2}-9-3x^{3}-x^{2}`
`=-2x^{4}-3x^{3}+(x^{2}-x^{2})-9`
`=-2x^{4}-3x^{3}-9`
`b//`
`P(x)+Q(x)=3x^{4}+5x^{3}-2x^{2}-x-2-2x^{4}-3x^{3}-9`
`=(3x^{4}-2x^{4})+(5x^{3}-3x^{3})-2x^{2}-x-(2+9)`
`=x^{4}+2x^{3}-2x^{2}-x-11`
`--------`
`P(x)-Q(x)=3x^{4}+5x^{3}-2x^{2}-x-2-(-2x^{4}-3x^{3}-9)`
`=3x^{4}+5x^{3}-2x^{2}-x-2+2x^{4}+3x^{3}+9`
`=(3x^{4}+2x^{4})+(5x^{3}+3x^{3})-2x^{2}-x+(9-2)`
`=5x^{4}+8x^{3}-2x^{2}-x+7`
`c//`
`2P(x)+5Q(x)=2(3x^{4}+5x^{3}-2x^{2}-x-2)+5(-2x^{4}-3x^{3}-9)`
`=6x^{4}+10x^{3}-4x^{2}-2x-4-10x^{4}-15x^{3}-45`
`=(6x^{4}-10x^{4})+(10x^{3}-15x^{3})-4x^{2}-2x-(4+45)`
`=-4x^{4}-5x^{3}-4x^{2}-2x-49`
`--------`
`4P(x)-3Q(x)=4(3x^{4}+5x^{3}-2x^{2}-x-2)-3(-2x^{4}-3x^{3}-9)`
`=12x^{4}+20x^{3}-8x^{2}-4x-8+6x^{4}+9x^{3}+27`
`=(12x^{4}+6x^{4})+(20x^{3}+9x^{3})-8x^{2}-4x+(27-8)`
`=18x^{4}+29x^{3}-8x^{2}-4x+19`
