Question

If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)

Answer 1

`-x^2+x-1`

Explanation:

Given functions are,

`f(x) = x^4 - x^3 + x^2`

`g(x) = -x^2`

Since,

`((f)/(g))(x)=(f(x))/(g(x))`

`=(x^4-x^3+x^2)/(-x^2)`

`=-(x^2(x^2-x+1))/(x^2)`

`=-(x^2-x+1)`

`=-x^2+x-1`

Hence, the value of (f/g)(x) is
`-x^2+x-1`

Answer 2

`f(x)=x^2-x^3+x^2=x^2(x^2-x+1)\\\\g(x)=-x^2\\\\\left((f)/(g)\right)(x)=(x^2(x^2-x+1))/(-x^2)=-x^2+x-1`