Question

Answer 1

`b,`

`f(x)-g(x)= (x^3-3x^2+6x-8)-(-6x^2+x^3-8+12x)`

`= x^3-3x^2+6x-8+6x^2-x^3+8-12x`

`= (x^3-x^3)+(-3x^2+6x^2)+(6x-12x)+(-8+8)`

`= 3x^2-6x`

`a,`

`f(x)+g(x)=(x^3-3x^2+6x-8)+(-6x^2+x^3-8+12x)`

`= x^3-3x^2+6x-8-6x^2+x^3-8+12x`

`=(x^3+x^3)+(-3x^2-6x^2)+(6x+12x)+(-8-8)`

`= 2x^3-9x^2+18x-16`

`c,`

`f(x)-g(x)=0`

`->  3x^2-6x=0`

`-> 3x*x - 3x*2 = 0`

`-> 3x(x-2)=0`

`->`\(\left[{}\begin{matrix}3x=0\\x-2=0\end{matrix}\right.\)

\(\rightarrow\left[{}\begin{matrix}x=0\\x=0+2\end{matrix}\right.\rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
`d,` Thay `x=1` vào đa thức

`f(1)=1^3+3*1^2+6*1-8`

`f(1)=1+3+6-8=4+6-8=10-8=2`