Đáp án+Giải thích các bước giải:

`c)`

`P(x)`

`f(x)=2x^4 −x^3 +7x−5 `

`g(x)=−x^2 +1`

`2f(x)=2(2x^4 −x^3 +7x−5)`

$ = 4x^4 - 2x^3 + 14x - 10$

`x^2 g(x)=x^2 (−x^2 +1)`

$ = -x^4 + x^2$

`P(x)=2f(x)−x^2 g(x)`

`P(x)=(4x^4 −2x^3 +14x−10)−(−x^4 +x^2 )`

`P(x)=4x64 −2x^3 +14x−10+x^4 −x^2`

`P(x)=5x^4 −2x^3 −x^2 +14x−10`

`d) `

`Q(x)`

`f(x)=2x^4 −x^3 +7x−5`

`g(x)=−x^2 +1`

`3x^2 g(x)=3x^2 (−x^2 +1) `

$ = -3x^4 + 3x^2$

`2f(x)=4x^4 −2x^3 +14x−10 `

`Q(x)=3x^2 g(x)−2f(x) `

`Q(x)=(−3x^4 +3x^2 )−(4x^4 −2x^3 +14x−10) `

`Q(x)=−3x^4 +3x^2 −4x^4 +2x^3 −14x+10 `

`Q(x)=−7x^4 +2x^3 +3x^2 −14x+10 `