Question

If f(x)=x^4-x^3+x^2 and g(x)=-x^2, where x =/= 0, what is (f/g)(x)?

Answer 1

- x² + x - 1

Explanation:

(f / g)(x)

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

divide each term on the numerator by - x²

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

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

= - x² + x -
`x^(0)` = - x² + x - 1