Question

[Hằng Phan]

Cho hai đa thức A(x) = 5x4 + 4x3 + 2x + 1 và B(x) = –5x4 + x3 + 3x2 + x – 1. a) Tìm đa thức M(x) sao cho M(x) - A(x) = B(x). b) Tìm đa thức N(x) sao cho N(x) = A(x) – B(x).

Answer 1

[Nguyễn Lê Phước Thịnh]

a: M(x)=5x^4+4x^3+2x+1-5x^4+x^3+3x^2+x-1

=5x^3+3x^2+3x

b: N(x)=5x^4+4x^3+2x+1+5x^4-x^3-3x^2-x+1

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

Answer 2

[『Kuroba ム Tsuki Ryoo ︵²ᵏ⁷』]

`@` `\text {dnammv}`

` \text {M(x)-A(x)=B(x)}`

`-> \text {M(x)=A(x)+B(x)}`

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

`= 5x^4 + 4x^3 + 2x + 1-5x^4 + x^3 + 3x^2 + x - 1`

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

`= 5x^3+3x^2+3x`

`b,`

`\text {N(x)=A(x)-B(x)}`

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

`= 5x^4 + 4x^3 + 2x + 1+5x^4 - x^3 - 3x^2 - x + 1`

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

`= 10x^4+3x^3-3x^2+x+2`