Question

Cho hai đa thức: A(x) = 4x⁴ + 6x² - 7x³ - 5x - 6 và B(x) = -5x² + 7x³ + 5x + 4 - 4x⁴.

a) Tìm đa thức M(x) sao cho M(x) = A(x) + B(x).

b) Tìm đa thức C(x) sao cho A(x) = B(x) + C(x).

c) M(1) , C(1)

Answer 1

a: M(x)=A(x)+B(x)

=4x^4-7x^3+6x^2-5x-6-4x^4+7x^3-5x^2+5x+4

=x^2-2

b: C(x)=A(x)-B(x)

=4x^4-7x^3+6x^2-5x-6+4x^4-7x^3+5x^2-5x-4

=8x^4-14x^3+11x^2-10x-10

c: M(1)=1^2-2=-1

C(1)=8-14+11-10-10=5-20=-15

Answer 2

`a,` 

\(M\left(x\right)=A\left(x\right)+B\left(x\right)=\left(4x^4+6x^2-7x^3-5x-6\right)+\)`(-5x^2+7x^3+5x+4-4x^4)`

`M(x)=4x^4+6x^2-7x^3-5x-6-5x^2+7x^3+5x+4-4x^4`

`=(4x^4-4x^4)+(-7x^3+7x^3)+(6x^2-5x^2)+(-5x+5x)+(-6+4)`

`=x^2-2`

`b,`

`A(x)=B(x)+C(x)`

`-> C(x)=A(x)-B(x)`

`-> C(x)=(4x^4 + 6x^2 - 7x^3 - 5x - 6)-(-5x^2+7x^3+5x+4-4x^4)`

`C(x)=4x^4 + 6x^2 - 7x^3 - 5x - 6+5x^2-7x^3-5x-4+4x^4`

`= (4x^4+4x^4)+(-7x^3-7x^3)+(6x^2+5x^2)+(-5x-5x)+(-6-4)`

`= 8x^4-14x^3+11x^2-10x-10`

`c,`

`M(1)=1^2-2=1-2=-1`

`C(1)=8*1^4-14*1^3+11*1^2-10*1-10`

`=8-14+11-10-10=-6+11-10-10=5-10-10=-5-10=-15`