Question

Answer 1

`a,`

\(P\left(x\right)=5x^5+4x^2+3x+6-4x^4-2x^3\)

`P(x)= 5x^5-4x^4-2x^3+4x^2+3x+6`

Bậc của đa thức: `5`

\(Q\left(x\right)=3x^2+2x^4+x+3-2x^3-x^5\)

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

Bậc của đa thức: `5`

`b,`

`P(x)-Q(x)=(5x^5-4x^4-2x^3+4x^2+3x+6)-(-x^5+2x^4-2x^3+3x^2+x+3)`

`= 5x^5-4x^4-2x^3+4x^2+3x+6+x^5-2x^4+2x^3-3x^2-x-3`

`= (5x^5+x^5)+(-4x^4-2x^4)+(-2x^3+2x^3)+(4x^2-3x^2)+(3x-x)+(6-3)`

`= 6x^5-6x^4+x^2+2x+3`

 

Ta có: `R(x)-P(x)=Q(x)`

`-> R(x)=Q(x)+P(x)`

`-> R(x)=(-x^5+2x^4-2x^3+3x^2+x+3)+(5x^5-4x^4-2x^3+4x^2+3x+6)`

`R(x)=-x^5+2x^4-2x^3+3x^2+x+3+5x^5-4x^4-2x^3+4x^2+3x+6`

`R(x)=(-x^5+5x^5)+(2x^4-4x^4)+(-2x^3-2x^3)+(3x^2+4x^2)+(x+3x)+(3+6)`

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